{
  "rules_version": "2",
  "validator_version": "r2.2",
  "prompt_version": "r2.1",
  "model": "gpt-5.5",
  "chemical_sha256": "528f1d8876aa85485b603dc4922d11966ce5806df9f1a094a3216a8843cdb220",
  "titles_sha256": "526d349ed8b111a6bde0a2f9b19a88def7f963c97785e52727a5450ab8bdd343",
  "items": [
    {
      "kind": "topic",
      "id": "amo.ultralight-dm-fifth-forces",
      "fields": {
        "why": {
          "text": "Atomic sensors are the only probes of dark matter much lighter than $10^{-10}$ eV and of new bosons coupling weakly to ordinary matter.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "astro.cosmic-ray-origins",
      "fields": {
        "summary": {
          "text": "Atomic nuclei reach Earth with energies up to $3 \\times 10^{20}\\,\\mathrm{eV}$, the kinetic energy of a thrown tennis ball packed into one particle. Which objects in our galaxy and beyond accelerate them is mostly unknown.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "astro.grb-engines-jets",
      "fields": {
        "summary": {
          "text": "Gamma-ray bursts are the brightest explosions known: beams of matter moving at over $99.99\\%$ of light speed, launched when a massive star collapses or two neutron stars merge. What powers the beam and what it is made of are unsettled.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "astro.high-energy-neutrino-sources",
      "fields": {
        "summary": {
          "text": "Neutrinos (nearly massless particles that pass through matter almost untouched) arrive from space with energies from about $10^{13}$ eV to about $2 \\times 10^{17}$ eV. Only a few sources have been identified, and most of the flux has no known origin.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "astro.pulsars-magnetars",
      "fields": {
        "why": {
          "text": "Pulsars are precise clocks used to detect gravitational waves, and their emission tests plasma physics in fields of $10^{12}\\,\\mathrm{G}$ and above.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "beams.nb3sn-cavities",
      "fields": {
        "title": {
          "text": "Performance gap of $\\mathrm{Nb_3Sn}$ cavities",
          "how": [
            "outside:chemical"
          ]
        },
        "summary": {
          "text": "$\\mathrm{Nb_3Sn}$ is a superconductor that could work at higher temperature and reach twice the field of niobium. Real $\\mathrm{Nb_3Sn}$ cavities reach well under half of that predicted field, for reasons not fully known.",
          "how": [
            "outside:chemical"
          ]
        },
        "why": {
          "text": "$\\mathrm{Nb_3Sn}$ cavities would allow compact accelerators cooled by simple cryocoolers and higher gradients for large linacs.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "chem.electrode-interfaces",
      "fields": {
        "why": {
          "text": "Hydrogen production, $\\mathrm{CO_2}$ conversion, fuel cells and batteries all depend on reactions in this layer.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.fese-sto-interface",
      "fields": {
        "title": {
          "text": "Interface superconductivity: FeSe/$\\mathrm{SrTiO_3}$ and $\\mathrm{KTaO_3}$",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.insulator-quantum-oscillations",
      "fields": {
        "summary": {
          "text": "In a metal, resistance and magnetization oscillate as a magnetic field is raised because mobile electrons move on closed orbits; an insulator has no mobile electrons, so this should not happen. Yet the Kondo insulators $\\mathrm{SmB_6}$ and $\\mathrm{YbB_{12}}$ and the two-dimensional insulator monolayer $\\mathrm{WTe_2}$ show such oscillations.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.moire-tmd-hubbard",
      "fields": {
        "summary": {
          "text": "Stacking two different semiconductor sheets, such as $\\mathrm{WSe_2}$ on $\\mathrm{WS_2}$ or $\\mathrm{MoTe_2}$ on $\\mathrm{WSe_2}$, creates a triangular grid of traps for electrons, a tunable version of the Hubbard model (electrons hopping between sites and repelling each other when they share one). Gates change the electron number and the hopping, so Mott insulators (insulators caused by repulsion), electron crystals and heavy-electron metals appear in one device.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.nickelates",
      "fields": {
        "summary": {
          "text": "Nickel oxides built like cuprates also superconduct: infinite-layer films such as Nd0.8Sr0.2NiO2 below about $15\\,\\mathrm{K}$ (near $40\\,\\mathrm{K}$ in samarium-based films), and bilayer $\\mathrm{La_3Ni_2O_7}$ near $80\\,\\mathrm{K}$ under about $140\\,\\mathrm{kbar}$ (up to about $96\\,\\mathrm{K}$ in 2025 reports), with onset above $60\\,\\mathrm{K}$ in compressed thin films at normal pressure. Why they superconduct, and how high the transition temperature $T_c$ can go, are open questions.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.phonon-thermal-hall",
      "fields": {
        "summary": {
          "text": "In a magnetic field, heat flowing through many electrical insulators is pushed sideways, even though the heat is carried by lattice vibrations (phonons) that have no charge. Why phonons respond to the field so strongly in materials as different as cuprates, $\\mathrm{SrTiO_3}$ and quartz is not understood.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.sr2ruo4",
      "fields": {
        "title": {
          "text": "Order parameter of the superconductor $\\mathrm{Sr_2RuO_4}$",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cm.twisted-tmd",
      "fields": {
        "title": {
          "text": "Twisted semiconductor bilayers $\\mathrm{MoTe_2}$ and $\\mathrm{WSe_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "summary": {
          "text": "Twisting two sheets of a semiconductor such as $\\mathrm{MoTe_2}$ or $\\mathrm{WSe_2}$ creates narrow electron bands whose electrons can show quantized Hall currents without an applied magnetic field, and can superconduct. These bands are topological: their wavefunctions have a winding that forces current-carrying states at the sample edges.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "cosmo.inflation",
      "fields": {
        "why": {
          "text": "Inflation links the largest structures to quantum physics at energies up to $\\sim 10^{16}\\,\\mathrm{GeV}$, far beyond any accelerator.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "earth.climate-sensitivity",
      "fields": {
        "summary": {
          "text": "Climate sensitivity is how much Earth eventually warms if the $\\mathrm{CO_2}$ in the air doubles. The answer is uncertain mostly because nobody knows well how clouds will change as the planet warms.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "hep.grand-unification",
      "fields": {
        "why": {
          "text": "Proton decay is the most direct test of unification at energies near $10^{16}\\,\\mathrm{GeV}$, far beyond any collider.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "hep.hierarchy-problem",
      "fields": {
        "summary": {
          "text": "The Higgs boson weighs about 130 times as much as a proton, yet quantum effects should push its mass up toward far heavier scales such as the Planck mass, about $10^{19}$ proton masses. Something must keep it light, and nobody knows what.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "topic",
      "id": "nuc.qcd-phase-diagram",
      "fields": {
        "summary": {
          "text": "At zero net baryon density, heating turns ordinary nuclear matter into a quark-gluon plasma smoothly, near $1.8 \\times 10^{12}\\,\\mathrm{K}$. At higher densities the change may become abrupt, and mapping where this happens is a central goal of the field.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.anderson-localization-3d.light-in-dielectrics",
      "fields": {
        "status_note": {
          "text": "A 2023 FDTD study found localization for random metallic sphere aggregates and none for dielectric spheres up to $n = 10$; earlier $\\mathrm{TiO_2}$ claims were attributed to fluorescence, and Skipetrov and Sokolov (Physical Review B 2025, https://doi.org/10.1103/t5nj-fz3p) predict localization for resonant impurities in a solid transparent matrix.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.attosecond-electron-dynamics.hhg-berry-curvature",
      "fields": {
        "precise": {
          "text": "In noncentrosymmetric materials (monolayer $\\mathrm{MoS_2}$, hBN, $\\alpha$-quartz) the anomalous velocity $v = -(e/\\hbar)\\ E\\ x\\ \\Omega(k)$, with $\\Omega(k)$ the Berry curvature, generates even-order harmonics polarized perpendicular to the drive. Question: can the perpendicular even-harmonic amplitudes and phases be inverted to give $\\Omega(k)$ along the driven trajectories with a stated accuracy, given interband contributions and propagation. An answer is a retrieval in a material with independently known Omega(k) that agrees within the stated uncertainty, or a proof that the inversion is not unique.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Retrievals were reported in $\\alpha$-quartz (Luu and Woerner, Nature Communications 2018) and even harmonics attributed to Berry curvature in $\\mathrm{MoS_2}$ (2017); uniqueness and model dependence of the inversion remain debated.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.attosecond-electron-dynamics.petahertz-switching-limits",
      "fields": {
        "precise": {
          "text": "Light-field-driven currents in dielectrics ($\\mathrm{SiO_2}$), graphene-gold junctions and metal nanoantenna tunnel junctions, switched within one optical cycle (frequency about $10^{15}\\,\\mathrm{s}^{-1}$). Quantities: the maximum switching bandwidth $f_{\\max}$ and minimum energy per switching event set by real versus virtual carrier populations, dephasing, heating and circuit parasitics, and whether a logic stage can drive the next one with gain above 1. An answer is a cascaded light-field-driven gate with measured gain above 1 at f above $10^{14}\\,\\mathrm{s}^{-1}$, or a derived bound that excludes it.",
          "how": [
            "inside:e-notation",
            "inside:operator-word",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.attosecond-electron-dynamics.solid-hhg-mechanism",
      "fields": {
        "precise": {
          "text": "Bulk or monolayer crystals (ZnO, $\\mathrm{SiO_2}$, GaSe, $\\mathrm{MoS_2}$) driven by a mid-infrared field with Keldysh parameter $\\gamma < 1$ below the damage threshold. Quantity: the fraction of the harmonic yield in each order from the interband polarization (electron-hole recollision) versus the intraband current (nonparabolic band motion, Bloch-like oscillation), as a function of order, field strength and wavelength. An answer is an experimental observable that separates the two contributions unambiguously (harmonic phase, ellipticity or two-color response) in at least one material, matched by a parameter-free microscopic calculation.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.bound-state-qed.proton-radius-residual",
      "fields": {
        "precise": {
          "text": "Muonic hydrogen gives $r_p = 0.84087(39)\\,\\mathrm{fm}$ and the 2026 hydrogen 2S-6P measurement (Maisenbacher et al) gives $0.8406(15)\\,\\mathrm{fm}$, while the LKB 1S-3S (2018), H 2S-8D (2022) and Mainz electron scattering ($0.879\\,\\mathrm{fm}$) determinations favor larger values. Establish whether all hydrogen lines, combined with 1S-2S, yield a single $(R_{\\infty}, r_{p})$ pair consistent at the $10^{-12}$ level in $R_{\\infty}$.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "A global fit of all hydrogen and deuterium transition frequencies, with outliers explained by identified systematics, giving $R_{\\infty}$ and $r_p$ consistent with muonic values within uncertainties.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.casimir-dispersion-forces.casimir-torque",
      "fields": {
        "precise": {
          "text": "Two uniaxial birefringent plates (e.g. calcite, quartz, black phosphorus) at gap $d$ across vacuum, with optic axes at relative angle $\\theta$: Lifshitz-type theory predicts torque per area $M(\\theta, d) \\sim A(d) \\sin(2\\theta)$, with $A(d)$ set by the anisotropic permittivities. An answer is a measurement of A(d) and the $\\sin(2\\theta)$ dependence at $d$ below about $10^{-4}\\,\\mathrm{cm}$, agreeing with theory using measured permittivity tensors.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.casimir-dispersion-forces.drude-plasma-puzzle",
      "fields": {
        "precise": {
          "text": "Lifshitz theory for Au or Ni sphere-plate geometries at $T = 300\\,\\mathrm{K}$ and separations $2 \\times 10^{-5}\\text{ to }10^{-4}\\,\\mathrm{cm}$: the Drude permittivity $\\epsilon(\\omega) = 1 - \\omega_p^2/(\\omega(\\omega + i \\gamma))$ removes the zero-frequency transverse-electric Matsubara term, while the plasma model ($\\gamma = 0$) keeps it. Micromechanical, dynamic AFM and isoelectronic differential measurements agree with the plasma model and exclude Drude, whereas a torsion-pendulum measurement at larger gaps (Sushkov et al., 2011) favored Drude after subtracting electrostatic patch forces. An answer is a physical mechanism (spatial dispersion, surface states, low-frequency response) that reproduces the data while staying consistent with measured optical and dc conductivity, confirmed at separations above $3 \\times 10^{-4}\\,\\mathrm{cm}$ where the thermal term is large.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A measurement of the thermal Casimir force at gaps above $3 \\times 10^{-4}$ cm with patch potentials characterized independently, plus a dielectric model that fits it and the metal's measured transport and optics.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.casimir-dispersion-forces.massive-mirror-dce",
      "fields": {
        "precise": {
          "text": "A mechanical mirror or membrane forming one wall of an electromagnetic cavity, oscillating at frequency $\\Omega$ with amplitude $a$; photon pairs are created at the cavity mode $\\omega = \\Omega/2$ at a rate set by $(a \\Omega / c)^{2}$ and the cavity quality factor. Mechanical resonators reach $\\Omega/2\\pi$ of order $10^{9} \\text{ to } 10^{10}\\,\\mathrm{s}^{-1}$ only with tiny amplitudes. An answer is detection of photon pairs from a mechanically moving body with rate and two-mode squeezing matching theory, separated from thermal and parametric backgrounds.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.cavity-photon-matter.equilibrium-superradiance",
      "fields": {
        "status_note": {
          "text": "No-go theorems hold for uniform fields; photon condensation is permitted for spatially varying fields as a magnetostatic instability (Andolina et al., PRB 2020); an equilibrium magnonic analog was reported in $\\mathrm{ErFeO_3}$ (Kim et al., Science Advances 2025), while a photonic equilibrium superradiant phase is unobserved.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.collective-emission.subradiant-scaling",
      "fields": {
        "status_note": {
          "text": "In $1\\mathrm{D}$, $\\gamma_{\\min} \\sim N^{-3}$ was found (Asenjo-Garcia et al., PRX 2017); $2\\mathrm{D}$ finite arrays lack an agreed exponent.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.constant-variation.alpha-drift-today",
      "fields": {
        "title": {
          "text": "Is $\\alpha$ drifting today at the $10^{-19}$ per year level?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Present laboratory bounds from optical clock ratios (for example the Yb+ E3/E2 comparison) give $\\left|\\mathrm{d}\\,\\mathrm{ln}(\\alpha)/\\mathrm{d}t\\right|$ of order $10^{-18}$ per year. Determine whether $\\mathrm{d}\\,\\mathrm{ln}(\\alpha)/\\mathrm{d}t$ is nonzero at the $10^{-19}$ per year level using multi-year ratios of clocks with large differential sensitivity, including the Th-229 nuclear transition.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "A multi-year ratio of a Th-229 nuclear clock (or highly charged ion clock) to an optical atomic clock with fractional uncertainty below $10^{-18}$, analyzed for a linear drift.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.constant-variation.mu-variation",
      "fields": {
        "precise": {
          "text": "Determine whether $\\mu = m_p/m_e$ varies, either as $d\\ln(\\mu)/dt$ today from comparisons of molecular (for example HD+, H2+, N2+, $\\mathrm{Sr_2}$) and atomic clocks, or as $\\Delta \\mu/\\mu$ at redshift $z > 1$ from $\\mathrm{H_2}$ and $\\mathrm{CH_3OH}$ absorption, at the $10^{-17}$ per year and $10^{-7}$ levels respectively.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "A molecular-clock to atomic-clock ratio tracked for several years with fractional uncertainty below $10^{-17}$, or a radio methanol absorption measurement with sub-$10^{-7}$ precision.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.constant-variation.quasar-alpha-dipole",
      "fields": {
        "precise": {
          "text": "Many-multiplet analyses of Keck and VLT spectra (Webb et al 2011) reported a dipole in $\\Delta \\alpha/\\alpha$ of order $10^{-5}$ across the sky at about $4\\sigma$; ESPRESSO measurements (Murphy et al 2022) found $\\Delta \\alpha/\\alpha = (1.3 \\pm 1.3\\,\\mathrm{stat} \\pm 0.4\\,\\mathrm{sys})\\,\\mathrm{ppm}$ toward HE0515-4414. Establish whether any spatial or redshift variation of $\\alpha$ exists at the $1\\,\\mathrm{ppm}$ level once wavelength-calibration, isotopic-abundance and blinding systematics are controlled.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.constant-variation.th229-alpha-sensitivity",
      "fields": {
        "status_note": {
          "text": "The 2024-2025 laser spectroscopy of Th-229 in $\\mathrm{CaF_2}$ established $K$ of order $10^{3}$ to $10^{4}$; the remaining uncertainty is about 40%.",
          "how": [
            "outside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.dipolar-supersolids.superfluid-fraction-2d",
      "fields": {
        "precise": {
          "text": "For a 2D triangular or honeycomb supersolid of Dy-164 or Er-166, measure the superfluid fraction tensor $f_{s},ij$ (via Josephson oscillations, moment of inertia or sound speeds) as a function of density contrast, and compare with Leggett's upper and lower bounds computed from the measured density profile. Answer: $f_{s},ij$ versus contrast with errors.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.efimov-universality.four-body-parameter",
      "fields": {
        "precise": {
          "text": "Zero-range theory predicts tetramer loss resonances at $a_{4},1 \\sim 0.43 a_{-}$ and $a_{4},2 \\sim 0.90 a_{-}$ (von Stecher, D'Incao, Greene 2009). With realistic van der Waals interactions, determine whether these ratios are universal to 5% or depend on short-range four-body physics. Answer: yes or no with a computed and measured spread across species.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.electric-dipole-moments.electron-edm",
      "fields": {
        "title": {
          "text": "Is the electron EDM nonzero above $10^{-31}$ e cm?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Current bound $\\mid d_{e}\\mid < 4.1 \\times 10^{-30}\\,e\\,\\mathrm{cm}$ (90% CL, JILA HfF+, 2023), with the Standard Model contribution many orders smaller. Determine whether $d_{e}$ (or the equivalent electron-nucleon coupling $C_{\\mathrm{S}}$) is nonzero at the $10^{-31}\\,e\\,\\mathrm{cm}$ level using polar molecules (ThO, ThF+, YbOH, BaF or others).",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A molecular EDM measurement with statistical and systematic uncertainty near $10^{-31}$ e cm, confirmed in a second species.",
          "how": [
            "outside:e-notation"
          ]
        },
        "status_note": {
          "text": "JILA's third-generation ThF+ experiment and ACME III (ThO) report progress toward roughly $10^{-31}$ e cm sensitivity as of 2026.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.electric-dipole-moments.neutron-edm",
      "fields": {
        "title": {
          "text": "Is the neutron EDM nonzero at the $10^{-27}$ e cm level?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "The best bound is $\\left|d_n\\right| < 1.8 \\times 10^{-26}\\,e\\,\\mathrm{cm}$ (90% CL, PSI 2020) using ultracold neutrons with a Hg-199 comagnetometer. Determine whether $d_n$ is nonzero at the $10^{-27}\\,e\\,\\mathrm{cm}$ level, which corresponds to the QCD vacuum angle $\\left|\\theta_{\\mathrm{bar}}\\right|$ of order $10^{-11}$ (using $d_n$ of about $10^{-16}\\,\\theta_{\\mathrm{bar}}\\,e\\,\\mathrm{cm}$).",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A neutron EDM measurement with total uncertainty near $10^{-27}$ e cm (n2EDM at PSI, or the US and Canadian ultracold-neutron efforts).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.fine-structure-constant.electron-g2-sm-test",
      "fields": {
        "precise": {
          "text": "With $g/2 = -\\mu_e/\\mu_B$ measured to 0.13 ppt ($a_e = (g-2)/2$ to 0.11 ppb, absolute uncertainty $1.3 \\times 10^{-13}$; Fan et al 2023) and $a_e(\\mathrm{SM})$ computed from $\\alpha(\\mathrm{recoil})$ plus QED (five-loop coefficient now agreed between two groups), hadronic and electroweak terms, determine whether $\\delta a_e = a_e(\\exp) - a_e(\\mathrm{SM})$ differs from zero; at present $\\delta a_e$ has opposite signs for $\\alpha(\\mathrm{Cs})$ and $\\alpha(\\mathrm{Rb})$, at roughly $-2.2\\ \\sigma$ and $+2\\ \\sigma$. The answer is $\\delta a_e$ with total uncertainty below $10^{-13}$ and its significance.",
          "how": [
            "inside:operator-word",
            "outside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Resolution of the Cs-Rb $\\alpha$ discrepancy combined with an improved $a_{e}$ measurement, yielding a single $\\delta a_{e}$ with uncertainty below $10^{-13}$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.fine-structure-constant.third-alpha-route",
      "fields": {
        "precise": {
          "text": "Determine $\\alpha$ with relative uncertainty below $10^{-10}$ using a method whose systematics are independent of Raman or Bragg recoil interferometry in alkali atoms, for example single-photon large-momentum-transfer interferometry in Sr or Yb, or helium $2^{3}P$ fine structure, which requires the $\\alpha^{8}m$ QED corrections (theory is complete at $\\alpha^{7}m$ since 2010) and resolution of the disagreement among helium $2^{3}P$ measurements. The answer is a value of $\\alpha^{-1}$ with uncertainty below $1.4 \\times 10^{-8}$.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.hubbard-simulation.certified-error-budget",
      "fields": {
        "precise": {
          "text": "Choose a point $(U/t, \\delta, T/t)$ where unbiased numerical methods lose control (for example $U/t = 8, \\delta = 0.1, T/t < 0.1$). Using Hamiltonian learning of $t, t', U$ and harmonic confinement, entropy thermometry, and stability bounds, give a certified error bar on the nearest-neighbour spin correlator $C(1,0)$ and on the density. Answer: an error budget with all sources listed and a total below $5\\%$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.hubbard-simulation.d-wave-pairing",
      "fields": {
        "precise": {
          "text": "Two-dimensional square-lattice Fermi-Hubbard model, $U/t = 6\\ \\text{to}\\ 8$, hole doping $\\delta = 0.1\\ \\text{to}\\ 0.2$, nearest-neighbour hopping $t$ and optional next-nearest hopping $t'$. Measure the d-wave pair correlation $P_d(r) = \\langle \\Delta_d^{\\mathrm{dag}}(r) \\Delta_d(0)\\rangle$, with $\\Delta_d(r)$ the d-wave singlet pair operator on the four bonds of site r, by quantum gas microscopy or pair-transport protocols at the lowest achievable $T/t$. True long-range order is excluded at $T > 0$ in 2D, so the answer is whether $P_d(r)$ decays algebraically below a Kosterlitz-Thouless temperature $T_{\\mathrm{KT}}$, or at least has a correlation length above 10 lattice sites, together with the temperature and entropy at which this appears.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.hubbard-simulation.doped-entropy-floor",
      "fields": {
        "precise": {
          "text": "Homogeneous (flat-bottom) 2D square-lattice Fermi-Hubbard sample with at least 100 sites, $U/t = 8$, hole doping $\\delta = 0.1\\ \\text{to}\\ 0.2$. Determine the minimum entropy per site $s_{\\min}$ (units of $k_{B}$) and temperature $T/t$ reachable by entropy redistribution into reservoirs and adiabatic loading, with independent thermometry, and identify the limiting heating processes (lattice-light scattering, technical noise, reservoir capacity). Answer: $s_{\\min}$ and $T/t$ in the doped region with an error budget, and whether $T/t < 0.05$ is reachable at $\\delta = 0.125$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.hubbard-simulation.entropy-threshold",
      "fields": {
        "precise": {
          "text": "Let $s_{\\exp}$ be the entropy per site (units of $k_B$) reached in current doped quantum-gas-microscope samples. For the 2D Hubbard model at $U/t = 8$, $\\delta = 0.125$, $t'/t = -0.2$, determine the entropy per site $s*$ below which the d-wave pair correlation length exceeds 10 lattice sites, and hence the required reduction $s_{\\exp} - s*$. Answer: $s*$ with error bars from controlled finite-temperature numerics and the ratio $s_{\\exp}/s*$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.hubbard-simulation.stripes-plain-2d",
      "fields": {
        "precise": {
          "text": "Square-lattice Fermi-Hubbard model with isotropic hopping, $U/t = 8 \\text{ to } 10$, $\\delta = 1/8$, $t'/t = 0 \\text{ and } -0.2$, imaged by quantum gas microscopy. Measure spin-spin and hole-hole correlation functions and determine whether unidirectional stripe correlations with wavelength set by the doping appear at the lowest accessible $T/t$ (about 0.05 to 0.1). Answer: stripe correlation length versus $T/t$ and $t'$, compared with finite-temperature numerics.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.lorentz-cpt.antihydrogen-1s2s",
      "fields": {
        "title": {
          "text": "Does antihydrogen 1S-2S match hydrogen at $10^{-15}$?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "ALPHA measured the antihydrogen $1\\mathrm{S}-2\\mathrm{S}$ two-photon frequency in agreement with hydrogen at about $2 \\times 10^{-12}$ relative precision (2018). Determine whether nu_1S2S(Hbar) - nu_1S2S(H) is nonzero at the $10^{-15}$ level, approaching the hydrogen precision of about 4e-15.",
          "how": [
            "outside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Antihydrogen 1S-2S spectroscopy with laser-cooled, magnetically trapped atoms reaching sub-kHz resolution and $10^{-15}$ accuracy.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.lorentz-cpt.antihydrogen-hyperfine",
      "fields": {
        "precise": {
          "text": "Measure the zero-field ground-state hyperfine splitting of antihydrogen (hydrogen: 1420.405751768 MHz) with relative uncertainty below $10^{-6}$, using either an in-beam Rabi method (ASACUSA) or trapped-atom microwave spectroscopy (ALPHA), and determine whether it differs from hydrogen.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.lorentz-cpt.antiproton-moment",
      "fields": {
        "title": {
          "text": "Proton and antiproton magnetic moments compared at $10^{-12}$",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "BASE compared proton and antiproton charge-to-mass ratios to 16 ppt (2022) and magnetic moments to about 1.5 ppb (2017). Determine whether $\\left|\\mu_{\\mathrm{pbar}}\\right|/\\mu_{\\mathrm{p}} - 1$ is nonzero at the $10^{-12}$ level, using sympathetic or quantum-logic cooling for faster single-spin-flip detection.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.lorentz-cpt.electron-anisotropy",
      "fields": {
        "title": {
          "text": "Are electron-sector Lorentz-violation coefficients nonzero at $10^{-23}$?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "In the Standard-Model Extension, the electron coefficients $c_{JK}$ (traceless symmetric) are bounded at about $10^{-21}$ by Yb+ E3 clock comparisons with orthogonal quantization axes (Sanner et al 2019). Determine whether any $c_{JK}$ is nonzero at the $10^{-23}$ level using highly charged ions or Dy and Yb+ states with large anisotropic momentum operators.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.macroscopic-optomechanics.csl-grw-test",
      "fields": {
        "precise": {
          "text": "Continuous spontaneous localization with rate $\\lambda$ and length $r_C$. Exclude $\\lambda = 10^{-16}\\ \\mathrm{s}^{-1}$ at $r_C = 10^{-5}\\ \\mathrm{cm}$ (the GRW value of Ghirardi, Rimini and Weber) by interferometric or non-interferometric (heating, noise) tests with massive objects. Answer: yes or no, with the excluded region in the $(\\lambda, r_C)$ plane.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "An interferometry or heating experiment whose excess-decoherence bound lies below $\\lambda$ = $10^{-16}$ $\\mathrm{s}^{-1}$ at $r_C$ = $10^{-5}$ cm.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.macroscopic-optomechanics.mechanical-cat-decoherence",
      "fields": {
        "precise": {
          "text": "Mechanical resonator of effective mass $m_{\\mathrm{eff}}$ in a cat state $\\left|\\alpha\\right> + \\left|-\\alpha\\right>$. Measure the cat decoherence rate $\\Gamma_{\\mathrm{cat}}$ versus $\\mid\\alpha\\mid^2$ and $m_{\\mathrm{eff}}$, and compare with the bath model $\\Gamma_{\\mathrm{cat}} = 2 \\mid\\alpha\\mid^2 \\Gamma_{\\mathrm{m}} (2 n_{\\mathrm{th}} + 1)$, with $\\Gamma_{\\mathrm{m}}$ the mechanical energy damping rate and $n_{\\mathrm{th}}$ the thermal phonon number, plus two-level-system defect noise. Answer: whether all decoherence is accounted for, and any excess as a function of mass.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.molecular-parity-violation.first-energy-difference",
      "fields": {
        "precise": {
          "text": "$\\Delta E_{\\mathrm{PV}} = E(R) - E(S)$ between enantiomers, or the corresponding difference in a vibrational or rotational transition frequency, $\\Delta \\nu/\\nu$. The best direct bound is at the $10^{-13}$ level of relative frequency for the C-F stretch of CHFClBr (Daussy et al., PRL 1999), several orders of magnitude above predictions for that molecule; heavy-atom candidates (Re, Os, Ru, W complexes, scaling roughly as $Z^5$) are predicted to be larger. An answer is a nonzero $\\Delta \\nu$ or $\\Delta E_{\\mathrm{PV}}$ with significance above $5\\,\\sigma$, with sign and magnitude compared to theory.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.molecular-parity-violation.homochirality-link",
      "fields": {
        "precise": {
          "text": "Predicted $\\Delta E_{\\mathrm{PV}}$ for amino acids and sugars corresponds to an equilibrium enantiomeric excess of order $10^{-17}$ at $300\\,\\mathrm{K}$ (estimate). Question: does any autocatalytic amplification mechanism (Frank-type autocatalysis with mutual inhibition, Kondepudi-Nelson bifurcation, Viedma ripening) under prebiotic conditions convert a bias of this size into a probability of selecting the natural handedness measurably different from $1/2$, given statistical fluctuations of order $N^{-1/2}$ in $N$ molecules and competing chiral biases (circularly polarized light, magnetochiral effects). An answer is a model with measured rate constants and volumes giving that probability, or an experiment showing PV-directed selection.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "Theoretical estimates place the PV-induced excess near $10^{-17}$ at 300 K; no experiment has shown PV-directed selection.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.muonic-atoms.muonic-hydrogen-hfs",
      "fields": {
        "precise": {
          "text": "Measure the $1\\mathrm{S}$ hyperfine transition of muonic hydrogen (about 0.18 eV, mid-infrared wavelength near 6.8 micron) with relative uncertainty of order $10^{-5}$ (FAMU goal) to $10^{-6}$ (CREMA goal), and extract the proton Zemach radius $r_Z$ and the polarizability part of the two-photon-exchange correction. The answer is $r_Z$ with uncertainty below 1% and a statement of whether it agrees with values from electron scattering and from the hydrogen 21 cm hyperfine splitting.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.muonic-atoms.muonium-spectroscopy",
      "fields": {
        "settled_by": {
          "text": "New muonium hyperfine and $1\\mathrm{S}-2\\mathrm{S}$ measurements, each with an uncertainty at least ten times below the 1999-2000 values, combined with bound-state QED theory to yield consistent $m_{\\mu}/m_e$ values.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.newtonian-g.atom-interferometer-g",
      "fields": {
        "precise": {
          "text": "Atom-interferometric gravity gradiometry with well-characterized source masses gave G with about 150 ppm uncertainty (Rosi et al 2014). Determine G with uncertainty below $10^{-5}$ relative by a cold-atom method, sufficient to discriminate among the discrepant macroscopic results.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.newtonian-g.measurement-spread",
      "fields": {
        "precise": {
          "text": "Laboratory determinations of G (torsion balances in time-of-swing, angular-acceleration and servo modes, beam balances, simple pendulums, atom interferometry) spread over about $5 \\times 10^{-4}$ relative, roughly ten times their typical quoted uncertainties of $10^{-5} \\text{ to } 5 \\times 10^{-5}$, near $G = 6.674 \\times 10^{-8}\\,\\mathrm{cm}^{3}\\,\\mathrm{g}^{-1}\\,\\mathrm{s}^{-2}$. Identify the unaccounted systematic effects (or establish any genuine dependence of the measured G on method, material or geometry) that explain the excess scatter.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A consensus set of independent measurements with different methods agreeing within quoted uncertainties at the $10^{-5}$ level, together with an identified correction to the outliers.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.newtonian-g.nist-bipm-gap",
      "fields": {
        "precise": {
          "text": "The NIST measurement (2026, Metrologia), using a torsion-strip balance of the BIPM design in both servo and Cavendish modes, gives $G = 6.67387 \\times 10^{-8}\\,\\mathrm{cm}^3\\,\\mathrm{g}^{-1}\\,\\mathrm{s}^{-2}$, about 235 ppm below the BIPM 2013 value. Identify the effect (mass metrology, torsion-strip anelasticity, source-mass density inhomogeneity, alignment, environment) that accounts for the difference.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.noisy-quantum-metrology.entangled-clock-frontier",
      "fields": {
        "precise": {
          "text": "Demonstrate an optical lattice or tweezer clock whose absolute fractional frequency instability, with entangled or squeezed atomic states, is below that of the best unentangled clock with the same atom number and interrogation hardware, at instability levels of order $10^{-17}$ at 1 s or better.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.optical-clocks-second.bbr-shift-1e19",
      "fields": {
        "title": {
          "text": "Blackbody radiation shift of lattice clocks at the $10^{-19}$ level",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Determine the room-temperature (300 K) blackbody shift of the Sr (or Yb) 1S0-3P0 lattice-clock transition, including the dynamic correction from the frequency dependence of the differential polarizability, with fractional uncertainty below $10^{-19}$, and the effective radiation temperature seen by the atoms to 10 mK.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.optical-clocks-second.redefinition-criteria",
      "fields": {
        "precise": {
          "text": "Determine whether the mandatory criteria of the CCTF roadmap (Dimarcq et al 2024), including repeated agreement of independent optical clocks and frequency ratios at the low-$10^{-18}$ level, continuous contributions to TAI and intercontinental comparisons at that level, are met by 2029 for one species or for an ensemble defining a weighted geometric-mean frequency.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.optical-clocks-second.remote-comparison",
      "fields": {
        "title": {
          "text": "Intercontinental optical clock comparison at $10^{-18}$",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Achieve a comparison of optical clocks separated by more than 5000 km with total uncertainty below $10^{-18}$, including link noise and the gravitational redshift ($1.1 \\times 10^{-18}$ per cm height), which requires geopotential differences known to $10^{3}\\,\\mathrm{cm}^2\\,\\mathrm{s}^{-2}$.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        },
        "settled_by": {
          "text": "An intercontinental clock comparison via free-space optical satellite link, transportable clocks or fiber, with an uncertainty budget below $10^{-18}$ and agreement with independent geodesy.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.optical-clocks-second.solid-state-nuclear-clock",
      "fields": {
        "precise": {
          "text": "For Th-229 in $\\mathrm{CaF_2}$, $\\mathrm{LiSrAlF_6}$ or $\\mathrm{ThF_4}$ hosts, identify the mechanisms (temperature-dependent electric-field gradients, inhomogeneous broadening from charge-compensating defects, isomer quenching by radiation-induced defects) limiting linewidth and frequency reproducibility, and determine the achievable fractional uncertainty of a solid-state nuclear clock.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "Repeated measurements across crystals and temperatures with a closed-loop nuclear clock compared to an optical clock, giving a reproducibility budget below $10^{-17}$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.optical-clocks-second.trapped-ion-nuclear-clock",
      "fields": {
        "precise": {
          "text": "Drive the $8.36\\,\\mathrm{eV}$ ($148.4\\,\\mathrm{nm}$) Th-229 isomer transition with a laser in a trapped, sympathetically cooled Th-229 ion (Th3+, whose single valence electron allows laser cooling and state detection, or higher charge states), detect excitation through the hyperfine structure of the electronic transitions, and determine the achievable systematic uncertainty of the resulting clock, predicted to approach $10^{-19}$ (Campbell et al, Physical Review Letters, 2012).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.quantum-equivalence-principle.antihydrogen-fall",
      "fields": {
        "precise": {
          "text": "ALPHA-g measured the vertical acceleration of antihydrogen as $a_g = (0.75 \\pm 0.13 stat+sys \\pm 0.16 simulation) g$ (2023). Determine $a_g/g$ with total uncertainty below 0.01 and test whether it differs from 1.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.quantum-equivalence-principle.atom-eotvos-1e15",
      "fields": {
        "title": {
          "text": "Atom-interferometric test of universality of free fall at $10^{-15}$",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Dual-species atom interferometry (Rb-85/Rb-87, Asenbaum et al 2020) bounds the Eotvos parameter $\\eta$ at about $10^{-12}$; MICROSCOPE bounds $\\eta(\\mathrm{Ti}, \\mathrm{Pt})$ at about $10^{-15}$ (2022). Determine $\\eta$ for a pair of quantum test masses with uncertainty at or below $10^{-15}$, for example in a $100\\,\\mathrm{m}$ class tower or in space.",
          "how": [
            "outside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A dual-species interferometer result for $\\eta$ with total uncertainty below $10^{-15}$ (MAGIS-100, AION, STE-QUEST class).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.quantum-equivalence-principle.superposition-wep",
      "fields": {
        "precise": {
          "text": "In the quantum formulation of the equivalence principle (Zych and Brukner, arXiv 1502.00971), the internal mass-energy operator $M = m_0 + H_{\\int}/c^2$ may couple to gravity through operators $M_g$ and $M_i$ that differ off-diagonally. Bound the off-diagonal violation parameters for atoms prepared in coherent superpositions of hyperfine or optical clock states at better than $10^{-12}$, improving on the about $10^{-9}$ bound of Rosi et al 2017.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "An atom interferometer with test atoms in clock-state superpositions measuring the differential acceleration with sub-$10^{-12}$ precision.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.simulator-verification.error-stable-observables",
      "fields": {
        "precise": {
          "text": "Local Hamiltonian $H$ on $N$ sites; the device implements $H+\\sum_i \\delta h_i$ with $\\mid\\mid \\delta h_i\\mid\\mid \\le \\epsilon$. Characterize the classes of states (Gibbs states at temperature T, quench dynamics to time t) and local observables O for which $\\left|\\langle O\\rangle_{\\mathrm{device}}-\\langle O\\rangle_{\\mathrm{ideal}}\\right|\\le f(\\epsilon,T,t)$ independent of $N$. Answer: theorems with explicit $f$, and counterexamples outside these classes.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.ultralight-dm-fifth-forces.monopole-dipole-nucleon",
      "fields": {
        "precise": {
          "text": "For the monopole-dipole potential $V(r) = g_s^{N} g_p^{N} (\\hbar^2/(8 \\pi m_N)) (\\sigma . r_{\\mathrm{hat}}) (1/(\\lambda r) + 1/r^2) \\exp(-r/\\lambda)$ between an unpolarized nucleon and a polarized nucleon (Moody-Wilczek form), with range $\\lambda$ from $10\\,\\text{micron}\\ \\text{to}\\ 1\\,\\mathrm{mm}$, determine whether $g_s^{N} g_p^{N}$ is nonzero down to the value expected for a QCD axion with a small CP-violating scalar coupling, using polarized He-3 or other nuclear-spin sensors near a modulated source mass (Arvanitaki and Geraci 2014).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.ultralight-dm-fifth-forces.oscillating-nucleon-edm",
      "fields": {
        "precise": {
          "text": "For axion dark matter with mass $m_a$ in $10^{-14} \\text{ to } 10^{-6}\\,\\mathrm{eV}$ and gluon coupling producing an oscillating $d_n \\sim 10^{-34}\\,e\\,\\mathrm{cm}$ at QCD-axion strength, determine whether an oscillating nucleon EDM or axion-nucleon gradient coupling is present at that strength, using solid-state NMR (CASPEr-type) or comagnetometers.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.ultralight-dm-fifth-forces.scalar-photon-coupling",
      "fields": {
        "precise": {
          "text": "For scalar dark matter $\\phi$ of mass $m_{\\phi}$ in $10^{-23}$ to $10^{-15}$ eV with local density $0.4\\,\\mathrm{GeV}\\,\\mathrm{cm}^{-3}$ and dimensionless linear coupling $d_{\\gamma}$ to the photon (called $d_e$ in the Damour-Donoghue convention, unrelated to the electron EDM), determine whether $d_{\\gamma}$ is nonzero below present limits from clock comparisons and the MICROSCOPE equivalence-principle bound, by searching for oscillations of optical-clock frequency ratios at angular frequency $m_{\\phi} c^2/\\hbar$.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.ultralight-dm-fifth-forces.stochastic-amplitude",
      "fields": {
        "precise": {
          "text": "For a virialized ultralight bosonic field with velocity dispersion about $10^{-3}\\,c$, the local amplitude is Rayleigh distributed when the measurement time $T$ is shorter than the coherence time $\\tau_c \\sim 10^{6}\\,h/(m c^2)$. Determine the correct likelihood and the resulting correction factor to exclusion limits for $T < \\tau_c$, including vector polarization and multi-sensor correlations.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "amo.unitary-fermi-transport.spin-diffusion-bound",
      "fields": {
        "precise": {
          "text": "Unitary Fermi gas in 3D (and 2D). Determine the minimum longitudinal spin diffusivity $D_s$ and transverse diffusivity $D_{\\perp}$ in units of $\\hbar/m$, and whether a universal bound $D \\ge c \\hbar/m$ holds. Answer: the value of $c$ for each, and a theory explaining the difference.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.accretion-jet-launching.ulx-super-eddington",
      "fields": {
        "precise": {
          "text": "Pulsating ultraluminous X-ray sources (M82 X-2, NGC 7793 P13, NGC 5907 ULX-1 with peak $L_X \\sim 10^{41}\\,\\mathrm{erg}/\\mathrm{s}$, several hundred times $L_{\\mathrm{Edd}}$ for $1.4\\,M_{\\mathrm{sun}}$) are accreting neutron stars. Decide among geometric beaming by optically thick wind funnels, magnetar-strength fields ($B > 10^{14}\\,\\mathrm{G}$) that suppress the electron-scattering cross section, and accretion columns with strong multipole fields. Answer: the beaming factor and surface field for each pulsating ULX, consistent with spin-up rate, pulsed fraction and isotropic calorimetry from surrounding nebulae.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.biosignatures.cosmic-shoreline",
      "fields": {
        "precise": {
          "text": "Test whether atmosphere retention among rocky exoplanets follows the cosmic shoreline relation $I \\text{ proportional to } v_{\\mathrm{esc}}^4$ ($I$ the cumulative XUV or bolometric instellation, $v_{\\mathrm{esc}}$ the escape speed) proposed from Solar System bodies, and measure its location and width for M-dwarf and FGK hosts. The answer is the boundary in the $(v_{\\mathrm{esc}}, I)$ plane with its scatter.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.biosignatures.eta-earth",
      "fields": {
        "precise": {
          "text": "Measure $\\eta_{\\mathrm{Earth}}$, the number per G and K dwarf of planets with $R = 0.5-1.5\\,R_{\\mathrm{earth}}$ in the conservative habitable zone. Kepler-based estimates span roughly 0.05-0.6 because of extrapolation in period and radius and stellar property uncertainties. The answer is a value with uncertainty below $\\sim 30\\%$.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.biosignatures.false-positives",
      "fields": {
        "precise": {
          "text": "Enumerate and quantify abiotic pathways that produce detectable $\\mathrm{O_2}$, $\\mathrm{O_3}$ or $\\mathrm{CH_4}$ plus $\\mathrm{CO_2}$ disequilibrium on rocky planets: $\\mathrm{H_2O}$ photolysis with hydrogen escape, $\\mathrm{CO_2}$ photolysis in dry atmospheres, serpentinization and volcanic outgassing. For each, derive spectral discriminants (CO, O4, $\\mathrm{H_2O}$ abundance, redox state) measurable by a Habitable Worlds Observatory-class telescope. The answer is a classified list with abundance ranges and discriminants.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.biosignatures.k2-18b-dms",
      "fields": {
        "precise": {
          "text": "K2-18 b is a temperate sub-Neptune ($R \\sim 2.6 R_{\\mathrm{earth}}, M \\sim 9 M_{\\mathrm{earth}}$) orbiting an M dwarf, with $\\mathrm{CH_4}$ and $\\mathrm{CO_2}$ detected by JWST in 2023. Determine whether dimethyl sulfide (and dimethyl disulfide) is present at $\\ge 5\\sigma$ in JWST NIRISS, NIRSpec and MIRI spectra, and if present, whether abiotic photochemistry or delivery can produce the inferred abundance.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.biosignatures.m-dwarf-atmospheres",
      "fields": {
        "status_note": {
          "text": "JWST 15 micron eclipse photometry in 2023 disfavors thick $\\mathrm{CO_2}$ atmospheres on TRAPPIST-1 b and c.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.circumgalactic-medium.cold-cloud-survival",
      "fields": {
        "precise": {
          "text": "Clouds at $T \\sim 10^{4}\\ \\mathrm{K}$ moving through halo gas at $T \\sim 10^{6}\\ \\mathrm{K}$ should be destroyed by Kelvin-Helmholtz instabilities in a few cloud-crushing times $t_{\\mathrm{cc}}$. Simulations find clouds grow when the mixing-layer cooling time is short compared with $t_{\\mathrm{cc}}$ (Gronke and Oh 2018). Determine whether this criterion, modified by magnetic fields, thermal conduction and cosmic rays, predicts the observed cloud sizes, velocities and covering fractions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.circumgalactic-medium.hot-halo-extent",
      "fields": {
        "precise": {
          "text": "Determine the electron density profile $n_{e}(r)$ and temperature of X-ray emitting gas ($T \\sim 10^{6}\\,\\mathrm{K}$) around galaxies with $M_{*} \\sim 3 \\times 10^{10}\\text{ to }10^{11}\\,M_{\\mathrm{sun}}$ out to the virial radius (about 250 kpc), including the slope (for example a beta-model with $\\beta \\sim 0.5$) and the total hot gas mass.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.circumgalactic-medium.missing-galactic-baryons",
      "fields": {
        "precise": {
          "text": "For halos of $M_h \\sim 10^{12}\\,M_{\\mathrm{sun}}$, stars and interstellar gas account for roughly 20 to 30 percent of $f_b M_h$ ($f_b \\sim 0.16$, the cosmic baryon fraction). Determine the mass in each phase of halo gas (cool $10^{4}\\,\\mathrm{K}$, warm $10^{5}\\,\\mathrm{K}$, hot above $10^{6}\\,\\mathrm{K}$) inside the virial radius and the mass ejected beyond it.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.compact-binary-origins.channel-fractions",
      "fields": {
        "settled_by": {
          "text": "Population inference on a catalog of order $10^{3}$ events with spin and eccentricity measurements that separate channel signatures.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.compact-binary-origins.common-envelope",
      "fields": {
        "precise": {
          "text": "In common-envelope evolution the orbital energy released during inspiral must unbind the donor envelope, conventionally parametrized by $\\alpha_{\\mathrm{CE}}\\times\\lambda$. Determine from $3D$ hydrodynamics (with recombination energy, jets and post-plunge evolution) whether envelopes of $15\\ \\text{to}\\ 40\\ M_{\\mathrm{sun}}$ red supergiant donors are fully ejected, and whether final separations of a few $R_{\\mathrm{sun}}$, small enough to merge by gravitational waves within $1.4 \\times 10^{10}\\ \\mathrm{yr}$, result. Answer: final separation and ejected mass versus donor mass and radius, and the implied share of mergers from this route versus stable mass transfer.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.compact-binary-origins.mass-peak-35",
      "fields": {
        "settled_by": {
          "text": "Measurement of the peak location versus redshift and spin with a catalog of order $10^{3}$ events, compared with channel predictions.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.compact-binary-origins.pair-instability-gap",
      "fields": {
        "precise": {
          "text": "Pair-instability and pulsational pair-instability supernovae predict no black holes from single-star collapse between $M_{\\mathrm{low}} \\sim 45 \\text{ to } 65\\,M_{\\mathrm{sun}}$ and $M_{\\mathrm{high}} \\sim 120 \\text{ to } 130\\,M_{\\mathrm{sun}}$, with $M_{\\mathrm{low}}$ sensitive to the $12\\mathrm{C}(\\alpha,\\gamma)16\\mathrm{O}$ rate and rotation. Determine $M_{\\mathrm{low}}$ and whether gap events (GW190521; GW231123 with components $\\sim 100 \\text{ to } 140\\,M_{\\mathrm{sun}}$ and spins $\\sim 0.8 \\text{ to } 0.9$) are hierarchical mergers, stellar-merger products, or evidence of a higher gap edge. Answer: inferred $M_{\\mathrm{low}}$ and a classification of gap events.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.core-collapse-supernovae.explosion-energy",
      "fields": {
        "plain": {
          "text": "Typical supernovae release about $10^{51}\\,\\mathrm{erg}$ as motion of the ejected gas; models must show that neutrino heating supplies this much.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "In $3\\mathrm{D}$ neutrino-radiation hydrodynamics with general relativity and energy-dependent neutrino transport, determine whether the delayed neutrino-heating mechanism reaches asymptotic explosion energies $\\sim 10^{51}\\,\\mathrm{erg}$ and Ni-56 masses $\\sim 0.01\\ \\text{to}\\ 0.1\\,M_{\\mathrm{sun}}$ (median $\\sim 0.03\\,M_{\\mathrm{sun}}$) for progenitors of $9\\ \\text{to}\\ 25\\,M_{\\mathrm{sun}}$, as observed in Type II-P supernovae. Answer: converged energies and Ni-56 masses versus progenitor, with dependence on resolution and transport method quantified.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "2024: $3\\mathrm{D}$ simulations followed for several seconds reach energies approaching $10^{51}\\ \\mathrm{erg}$ for some progenitors; code-to-code agreement is not established.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.core-collapse-supernovae.neutron-star-kicks",
      "fields": {
        "precise": {
          "text": "Determine whether asymmetric mass ejection (gravitational tug of slow ejecta) and anisotropic neutrino emission in 3D explosions reproduce the pulsar velocity distribution (mean $\\sim 4 \\times 10^{7}\\ \\mathrm{cm/s}$, tail above $10^{8}$ cm/s), birth spin periods (tens to hundreds of ms) and any spin-kick alignment. Answer: predicted distributions from simulation suites compared with pulsar proper motions.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.core-collapse-supernovae.precursor-mass-loss",
      "fields": {
        "precise": {
          "text": "Early spectra with narrow, short-lived emission lines (flash ionization) show dense circumstellar material within $\\sim 10^{15}\\,\\mathrm{cm}$ in a large fraction of Type II supernovae, implying mass-loss rates $\\sim 10^{-4}$ to $10^{-2}$ $M_{\\mathrm{sun}}/\\mathrm{yr}$ in the last years, far above steady red supergiant winds of $\\sim 10^{-6}$ $M_{\\mathrm{sun}}/\\mathrm{yr}$. Identify the mechanism (wave energy transport from core convection in the last burning stages, binary interaction, pulsation-driven winds) and whether it also produces observed pre-explosion outbursts. Answer: a mechanism predicting circumstellar mass and extent versus progenitor mass and evolutionary stage.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.core-collapse-supernovae.slsn-power",
      "fields": {
        "precise": {
          "text": "Type I superluminous supernovae peak at $L \\sim 10^{44}\\,\\mathrm{erg}/\\mathrm{s}$ and radiate $\\sim 10^{51}\\,\\mathrm{erg}$. Decide among spin-down of a millisecond magnetar $(P \\sim 1\\ \\text{to}\\ 5\\,\\mathrm{ms}, B \\sim 10^{14}\\,\\mathrm{G})$, interaction with hydrogen-poor circumstellar shells, and pair-instability explosions, using late-time light-curve slopes, light-curve bumps, nebular spectra and late radio or X-ray emission from a central nebula. Answer: the power source for each subclass with the evidence.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.core-collapse-supernovae.sn1987a-remnant",
      "fields": {
        "precise": {
          "text": "Determine whether the compact object in SN 1987A is a cooling neutron star or powers a pulsar wind nebula, and constrain its spin and magnetic field, from the JWST-detected narrow argon lines near the center, the disputed 2021-2022 hard X-ray detections attributed to a pulsar wind nebula, and ALMA dust constraints. Answer: an identification with a luminosity budget of $\\sim 10^{35}\\ \\text{to}\\ 10^{36}\\,\\mathrm{erg/s}$ consistent with all bands.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.auger-ta-discrepancy",
      "fields": {
        "title": {
          "text": "Why do Auger and Telescope Array spectra differ above $3 \\times 10^{19}\\,\\mathrm{eV}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "After cross-calibration of energy scales, the Telescope Array flux above $\\sim 3 \\times 10^{19}\\ \\mathrm{eV}$ and its suppression energy remain higher than those of the Pierre Auger Observatory. Determine whether the residual difference is instrumental (energy-scale nonlinearity, aperture, atmospheric corrections) or a real dependence on sky direction that would imply a nearby source in the northern sky. Answer: yes or no for a direction-dependent flux, with significance after systematics, evaluated in the declination band seen by both.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.galactic-extragalactic-transition",
      "fields": {
        "plain": {
          "text": "Below some energy cosmic rays come from our own galaxy and above it from other galaxies; whether the handover happens near $10^{17}\\,\\mathrm{eV}$ or near $5 \\times 10^{18}\\,\\mathrm{eV}$ (the ankle, where the spectrum flattens) is unsettled.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Determine the energy at which the extragalactic flux exceeds the Galactic flux, using the iron knee near $8 \\times 10^{16}\\,\\mathrm{eV}$, the second knee near $10^{17}\\text{ to }3 \\times 10^{17}\\,\\mathrm{eV}$, the ankle near $5 \\times 10^{18}\\,\\mathrm{eV}$, the energy dependence of the mean shower depth $X_{\\max}$ and its spread (lightest composition near $2 \\times 10^{18}\\,\\mathrm{eV}$), and the change of the dipole direction from near the Galactic center below $10^{18}\\,\\mathrm{eV}$ to away from it above $8 \\times 10^{18}\\,\\mathrm{eV}$. Answer: the transition energy and the Galactic component spectrum, including whether a second Galactic population beyond the knee sources is required.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "Mass-resolved spectra and anisotropies from $10^{16} \\text{ to } 10^{19}\\,\\mathrm{eV}$ with overlapping detectors, fit by a two-population model with propagation.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.knee-origin",
      "fields": {
        "plain": {
          "text": "The number of cosmic rays falls off faster above about $3 \\times 10^{15}\\,\\mathrm{eV}$, a feature called the knee, which may mark the highest energy the Milky Way's particle accelerators reach.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "The all-particle spectrum steepens from dN/dE ~ E^-2.7 to ~E^-3.1 near $E \\sim 3-4\\,\\mathrm{PeV}$, and LHAASO finds that the proton spectrum hardens and then breaks sharply near 3 PeV. Determine which Galactic source class (supernova remnants, young massive star clusters, microquasars, the Galactic center) accelerates protons to at least 3 PeV, and whether the knee is a source maximum-rigidity feature ($E_{\\max}$ proportional to charge $Z$) or a propagation feature. Answer: an identified PeVatron class with an acceleration model reproducing the proton and helium knee positions.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.muon-puzzle",
      "fields": {
        "precise": {
          "text": "Auger (2016) found the muon number in showers near $10^{19}\\,\\mathrm{eV}$ larger than simulations with LHC-tuned hadronic models (EPOS-LHC, QGSJetII-04) by factors of about 1.3 to 1.6, and a combined analysis of several experiments finds a deficit in simulations that grows with energy above $\\sim 10^{16}\\,\\mathrm{eV}$. Identify the missing physics in hadronic interaction models (enhanced strangeness or baryon production, reduced neutral-pion fraction, forward-region effects) consistent with collider data. Answer: a modified model reproducing muon number, $X_{\\max}$ and muon production depth at once, with the resulting shift in inferred composition.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.suppression-cause",
      "fields": {
        "title": {
          "text": "Is the cosmic-ray flux cutoff above $4 \\times 10^{19}\\,\\mathrm{eV}$ a GZK effect?",
          "how": [
            "inside:e-notation"
          ]
        },
        "plain": {
          "text": "Very few cosmic rays arrive above about $4 \\times 10^{19}$ eV, either because they lose energy on the leftover light of the Big Bang (the GZK effect) or because their sources cannot push them higher.",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Determine whether the suppression of the ultra-high-energy cosmic-ray flux at $E > \\sim 4 \\times 10^{19}\\,\\mathrm{eV}$ is mainly due to propagation losses (photopion production on the cosmic microwave background for protons, photodisintegration for nuclei) or to source maximum rigidity of a few $10^{18}\\,\\mathrm{V}$ with composition getting heavier at higher energy. Answer: yes or no for a dominant GZK origin, with the proton fraction above $5 \\times 10^{19}\\,\\mathrm{eV}$ and the implied cosmogenic neutrino flux.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.cosmic-ray-origins.uhecr-sources",
      "fields": {
        "title": {
          "text": "Which sources accelerate cosmic rays above $10^{19}\\,\\mathrm{eV}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "For $E > 8 \\times 10^{18}\\ \\mathrm{eV}$ (Auger large-scale dipole, amplitude $\\sim 6.5\\%$, pointing away from the Galactic center) and $E > 4 \\times 10^{19}\\ \\mathrm{eV}$ (intermediate-scale excesses near Centaurus A and starburst galaxies for Auger, the hotspot for Telescope Array), identify the source population (AGN jets, starburst galaxies, gamma-ray bursts, tidal disruption events, magnetars). Answer: a source class whose emissivity, maximum rigidity and composition reproduce the spectrum, the shower-depth ($X_{\\max}$) distributions and the arrival-direction anisotropies after propagation through Galactic and extragalactic magnetic fields.",
          "how": [
            "inside:e-notation",
            "inside:operator-word",
            "inside:percent"
          ]
        },
        "settled_by": {
          "text": "Per-event mass estimates above $4 \\times 10^{19}\\,\\mathrm{eV}$ (AugerPrime) allowing light nuclei to be traced back, together with a $5\\sigma$ intermediate-scale anisotropy associated with a source catalog.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "2023: Telescope Array reported a $2.4 \\times 10^{20}\\ \\mathrm{eV}$ event (Amaterasu) whose arrival direction points toward the Local Void with no plausible nearby source.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.disk-dynamics.bar-slowdown",
      "fields": {
        "precise": {
          "text": "Dynamical friction with a cold dark matter halo should slow bars to $R = R_{\\mathrm{CR}}/R_{\\mathrm{bar}} > 1.4$ ($R_{\\mathrm{CR}}$ is the corotation radius), while most measured bars have $R < 1.4$. Decide whether observed bar pattern speeds and their evolution, including the Milky Way bar's slowing inferred from the kinematics and metallicity of stars trapped at its corotation resonance, which include the Hercules moving group (Chiba, Friske and Schoenrich 2021; Chiba and Schoenrich 2021), are consistent with $\\Lambda-\\mathrm{CDM}$ halos, and if not whether measurement biases or modified halo physics explain the gap.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.fast-radio-bursts.emission-site",
      "fields": {
        "precise": {
          "text": "Decide between emission at $r < \\sim 10^{10}\\,\\mathrm{cm}$ inside a magnetosphere (coherent curvature or plasma emission) and emission at $r \\sim 10^{13}\\ \\text{to}\\ 10^{15}\\,\\mathrm{cm}$ by synchrotron maser emission at a relativistic magnetized shock. Discriminants: emission-region size from scintillation, polarization-angle swings within bursts, microsecond structure and spectral bandwidth. Answer: the site for each burst subclass, with the evidence.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "2025: scintillation of FRB 20221022A limited its emission region to below about $3 \\times 10^{9}\\,\\mathrm{cm}$, and a pulsar-like polarization-angle swing of about 130 degrees was found in the same burst, favoring a magnetospheric origin for that event; whether this holds for other bursts is open.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.fast-radio-bursts.old-hosts",
      "fields": {
        "plain": {
          "text": "Some bursts come from a globular cluster (a ball of stars about $10^{10}\\,\\mathrm{years}$ old) or from galaxies that stopped forming stars long ago, where newborn magnetars should be absent.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.fast-radio-bursts.persistent-radio-sources",
      "fields": {
        "precise": {
          "text": "FRB 20121102A and FRB 20190520B are co-located with compact persistent radio sources (spectral luminosity $\\sim 10^{29}\\,\\mathrm{erg}\\,\\mathrm{s}^{-1}\\,\\mathrm{Hz}^{-1}$, size below $\\sim 1\\,\\mathrm{pc}$) and show rotation measures up to $\\sim 10^{5}\\,\\mathrm{rad}\\,\\mathrm{m}^{-2}$ that change by tens of percent over years. Determine whether these sources are magnetar wind nebulae, nebulae inflated by hyper-accreting compact binaries, or accreting intermediate-mass or massive black holes, and test the predicted relation between persistent-source luminosity and $\\mid \\mathrm{RM} \\mid$. Answer: an identification whose predicted decline of persistent flux and RM over decades matches monitoring.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.fast-radio-bursts.source-population",
      "fields": {
        "plain": {
          "text": "One magnetar in our own galaxy (a neutron star with a magnetic field of about $2 \\times 10^{14}\\ \\mathrm{G}$) has emitted an FRB-like burst, but it is unknown whether magnetars make all FRBs. Bursts also come from an old star cluster and from dead galaxies, where young magnetars should be rare.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Given the observed FRB population (all-sky rate of order $10^{3}\\,\\text{per day}$ above a few Jy ms at $600\\,\\mathrm{MHz}$, isotropic energies $10^{36} \\text{ to } 10^{43}\\,\\mathrm{erg}$, hosts ranging from star-forming spirals to quiescent ellipticals and a globular cluster of M81), determine which source classes produce it and in what proportions. An answer is a population model (young magnetars, merger-formed or accretion-induced neutron stars, accreting compact binaries, other) that reproduces the energy function, repetition statistics, and host and offset distributions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.first-smbh.overmassive-black-holes",
      "fields": {
        "precise": {
          "text": "For broad-line AGN at $z > 4$, including little red dots, determine whether $M_{\\mathrm{BH}}/M_{*}$ exceeds the local value $\\sim 10^{-3}$ by factors 10-100 as single-epoch virial estimates ($M_{\\mathrm{BH}}$ from FWHM of $\\mathrm{H}-\\alpha$ or $\\mathrm{H}-\\beta$ and luminosity) imply, or whether electron scattering and radiative transfer in dense gas broaden the lines and inflate $M_{\\mathrm{BH}}$. The answer is a calibrated $M_{\\mathrm{BH}}-M_{*}$ relation at $z > 4$ with $M_{\\mathrm{BH}}$ measured independently of the virial line-width method.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galactic-gamma-ray-anomalies.bulge-msp-census",
      "fields": {
        "precise": {
          "text": "The pulsar explanation requires a bulge population whose gamma-ray luminosity function matches the excess, implying a definite number of millisecond pulsars above the flux limits of MeerKAT, FAST and SKA-Mid bulge surveys (down to $\\sim 10^{-5}\\ \\mathrm{Jy}$ at 1.4 GHz). Determine the number detected and whether it agrees within a factor of 2 with the population required. Answer: yes or no with the count.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galactic-gamma-ray-anomalies.gev-excess-origin",
      "fields": {
        "plain": {
          "text": "Fermi satellite data show extra gamma rays near $2 \\times 10^{9}\\ \\mathrm{eV}$ from the inner galaxy, which could come from annihilating dark-matter particles or from a large hidden population of millisecond pulsars (old, fast-spinning neutron stars).",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "The Fermi-LAT excess (spectrum peaking near $1\\text{ to }3\\,\\mathrm{GeV}$, extending $\\sim 10\\text{ to }20\\,\\mathrm{deg}$ from the Galactic center, luminosity of order $10^{37}\\,\\mathrm{erg/s}$) fits either dark-matter annihilation (mass $\\sim 30\\text{ to }70\\,\\mathrm{GeV}$ into b quarks, $\\langle \\sigma v\\rangle \\sim 2 \\times 10^{-26}\\,\\mathrm{cm}^3/\\mathrm{s}$) or tens of thousands of unresolved bulge millisecond pulsars. Determine which. Answer: an identification at $5\\sigma$ from morphology, photon-count statistics, radio pulsar counts, or matching signals in dwarf galaxies.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galactic-gamma-ray-anomalies.positron-origin",
      "fields": {
        "plain": {
          "text": "About $5 \\times 10^{43}$ positrons per second annihilate in the Milky Way, mostly in the central bulge, and no known source class explains both the rate and the bulge-heavy pattern.",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Explain the $511\\,\\mathrm{keV}$ line (annihilation rate $\\sim 5 \\times 10^{43}\\,\\mathrm{positrons}/\\mathrm{s}$, bulge-to-disk luminosity ratio $\\sim 1$) with positrons injected below a few MeV (required by in-flight annihilation limits). Candidates: beta-plus decay of $\\mathrm{Al}-26$, $\\mathrm{Ti}-44$ and $\\mathrm{Co}-56$ from supernovae and novae, microquasars and low-mass X-ray binaries, past activity of Sgr A*, MeV-mass dark matter. Answer: a source mixture reproducing rate, morphology and spectrum, including positron transport.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galactic-gamma-ray-anomalies.positron-propagation",
      "fields": {
        "precise": {
          "text": "Determine the distribution of propagation distances of positrons born at energies below a few MeV in the warm, hot and neutral phases of the interstellar medium, with slowing-down times of $\\sim 10^{5}\\text{ to }10^{7}\\,\\mathrm{yr}$ and realistic magnetic turbulence. Answer: the fraction of disk-born positrons that annihilate in the bulge, compared with the observed bulge-to-disk ratio and line width.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galaxy-quenching.cooling-flow",
      "fields": {
        "precise": {
          "text": "In cool-core clusters the central gas has cooling time $t_{\\mathrm{cool}}<1\\ \\mathrm{Gyr}$ within $\\sim 100\\ \\mathrm{kpc}$, while star formation rates are $\\sim 1\\text{-}10\\%$ of classical cooling-flow rates of $10^2\\text{-}10^3\\ M_{\\mathrm{sun}}/\\mathrm{yr}$. Determine how jet mechanical power $P_{\\mathrm{jet}}\\sim 10^{44}\\text{-}10^{46}\\ \\mathrm{erg/s}$ is converted to heat nearly isotropically: weak shocks, sound waves, turbulent dissipation, cosmic-ray heating, or turbulent mixing. The answer is the heating rate per channel versus radius matched to the cooling rate.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.galaxy-quenching.m-sigma-origin",
      "fields": {
        "precise": {
          "text": "Classical bulges and ellipticals follow $M_{\\mathrm{BH}} \\sim \\sigma^{\\beta}$ with $\\beta \\sim 4-5$ and intrinsic scatter ~ 0.3 dex in $\\log M_{\\mathrm{BH}}$, while pseudobulges and disks do not follow it tightly (Kormendy and Ho 2013, arXiv:1304.7762). Determine the origin: self-regulation by AGN momentum- or energy-driven winds (predicting a definite $\\beta$ and normalization), central-limit averaging through successive mergers, or a common gas supply. The answer is a mechanism whose predicted redshift evolution of slope, normalization and scatter matches measurements.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.grb-engines-jets.engine-identity",
      "fields": {
        "precise": {
          "text": "For long and short GRBs, determine whether the engine is a millisecond proto-magnetar (rotational energy at most $\\sim 2 \\times 10^{52}\\ \\mathrm{erg}$, X-ray plateau followed by $L\\sim t^{-2}$ decay) or a hyperaccreting black hole (Blandford-Znajek power with fall-back accretion L ~ t^-5/3). Answer: per-burst engine classification with energy budget, using X-ray plateaus, extended emission and late flares.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Beaming-corrected jet energies above $2 \\times 10^{52}\\,\\mathrm{erg}$ excluding magnetars for a burst subclass, and gravitational-wave detection of the post-merger remnant for short bursts.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.grb-engines-jets.jet-composition",
      "fields": {
        "precise": {
          "text": "Determine the magnetization $\\sigma = B'^{2}/(4\\pi\\rho' c^{2})$, with B' the comoving magnetic field and rho' the comoving rest-mass density, of GRB jets at the dissipation radius $r \\sim 10^{13} \\text{ to } 10^{16}\\,\\mathrm{cm}$, distinguishing Poynting-dominated ($\\sigma >> 1$) from fireball ($\\sigma << 1$) jets, using the strength of a thermal photospheric component, prompt gamma-ray polarization degree and early reverse-shock optical emission. Answer: $\\sigma$ at the emission radius for the bulk of bursts, with evidence.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.grb-engines-jets.tev-afterglow",
      "fields": {
        "plain": {
          "text": "Some bursts emit photons above $10^{12}\\,\\mathrm{eV}$ for hours after the explosion, more energetic than electrons spiraling in the shock's magnetic field are thought able to make.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.high-energy-neutrino-sources.diffuse-flux-origin",
      "fields": {
        "precise": {
          "text": "The IceCube diffuse astrophysical flux (per-flavor $E^2 \\Phi$ of about $10^{-8}\\,\\mathrm{GeV}\\,\\mathrm{cm}^{-2}\\,\\mathrm{s}^{-1}\\,\\mathrm{sr}^{-1}$ near 100 TeV, spectral index $\\sim 2.4\\ \\text{to}\\ 2.9$) is not accounted for by gamma-ray blazars (stacking limits of order 10 percent) or by the Galactic plane (of order 10 percent near 30 TeV). Identify the population or populations producing most of it, including gamma-ray-dark sources such as Seyfert coronae, consistent with the isotropic gamma-ray background. Answer: source classes with flux fractions summing to the observed flux.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.high-energy-neutrino-sources.km3-event",
      "fields": {
        "settled_by": {
          "text": "Joint IceCube-KM3NeT analysis with added exposure, and detection or exclusion of further events above $10^{17}\\,\\mathrm{eV}$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.high-energy-neutrino-sources.seyfert-coronae",
      "fields": {
        "precise": {
          "text": "For NGC 1068 (neutrino luminosity $\\sim 3 \\times 10^{42}\\ \\mathrm{erg}/\\mathrm{s}$ at 1.5-15 TeV, with a GeV-TeV gamma-ray flux far lower), determine where and how protons are accelerated to $\\sim 10^{14}\\ \\mathrm{eV}$ within $\\sim 10\\ \\text{to}\\ 100$ gravitational radii of the black hole (turbulent acceleration, magnetic reconnection, accretion shocks), and whether the model predicts how neutrino luminosity scales with intrinsic X-ray luminosity across Seyferts. Answer: a model giving $L_{\\nu}/L_{X}$ and the spectral shape, tested against the Seyfert sample.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.high-energy-neutrino-sources.txs-0506-flare",
      "fields": {
        "precise": {
          "text": "IceCube-170922A coincided with a gamma-ray flare of TXS 0506+056 (about $3\\sigma$), while archival data show an excess of $13 \\pm 5$ neutrinos in 2014-2015 ($3.5\\sigma$) with no rise in gamma rays. One-zone lepto-hadronic models cannot give that neutrino luminosity without overproducing X rays and gamma rays from cascades. Determine the emission geometry (multiple zones, a compact core dense in target photons, jet interaction with clouds or stars) that fits both episodes, and whether it allows gamma-ray blazars to supply more than $\\sim 10\\%$ of the diffuse flux. Answer: a model fitting both episodes and the multiwavelength data.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.interstellar-objects.composition",
      "fields": {
        "status_note": {
          "text": "JWST spectra in 2025 showed a $\\mathrm{CO_2}$-dominated coma of 3I/ATLAS ($\\mathrm{CO2}/\\mathrm{H2O} \\sim 8$), VLT spectra detected nickel vapor with little or no iron, and its non-gravitational acceleration near perihelion is attributed to outgassing.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.interstellar-objects.oumuamua-acceleration",
      "fields": {
        "precise": {
          "text": "1I/'Oumuamua showed a radial non-gravitational acceleration of approximately $5x10^{-4}\\ \\mathrm{cm}/\\mathrm{s}^2$ at $1\\ \\mathrm{AU}$ scaling roughly as $r^{-2}$, with no detected coma and tight limits on CO, $\\mathrm{CO_2}$ and dust. Identify the cause: $\\mathrm{H_2}$ outgassing from radiolytically processed water ice, $\\mathrm{N_2}$ or $\\mathrm{H_2}$ ice composition, or radiation pressure on a very low-density body, consistent with its light curve, size and thermal limits.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "A model that fits the acceleration, the absence of detected gas and dust, and the light curve, tested on future similar objects with spectroscopic sensitivity to $\\mathrm{H_2}$ and $\\mathrm{N_2}$ outgassing.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.ism-astrochemistry.cold-cloud-pahs",
      "fields": {
        "precise": {
          "text": "In TMC-1 (T ~ 10 K, n_H2 $\\sim 10^{4}$ cm^-3) radio spectroscopy has detected complex organic molecules and cyano-substituted polycyclic aromatic hydrocarbons (cyanonaphthalenes, 2021; cyanopyrene, 2024; cyanocoronene, 2025) at abundances orders of magnitude above bottom-up gas-grain models. Identify the formation pathways (barrierless gas-phase growth, grain-surface chemistry with nonthermal desorption, or inheritance from an earlier phase) that reproduce the observed abundances.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.ism-astrochemistry.cr-ionization-rate",
      "fields": {
        "precise": {
          "text": "H3+ absorption gives a mean primary ionization rate per $\\mathrm{H_2}$ molecule $\\zeta_2 \\sim 3.5 \\times 10^{-16}\\,\\mathrm{s}^{-1}$ in diffuse molecular clouds (Indriolo and McCall 2012), more than 10 times the rate implied by the local interstellar cosmic-ray spectrum measured by Voyager 1. Determine the cause: a spatially variable low-energy (1 to 100 MeV) cosmic-ray population, nearby sources, or errors in the H3+ chemistry.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.neutron-star-interiors.cas-a-cooling",
      "fields": {
        "precise": {
          "text": "Chandra spectra of the Cas A neutron star (age about $340\\ \\mathrm{yr}$) have been fit with a surface temperature decline of approximately 1 to 4 percent per decade, the value and significance depending on detector mode, calibration and interstellar absorption modeling. Determine $dT_{s}/dt$ with systematics, and decide whether it requires neutrino emission from Cooper-pair formation at the onset of neutron triplet superfluidity (critical temperature of order $5 \\times 10^{8}\\text{ to }10^{9}\\ \\mathrm{K}$) or permits slower standard cooling.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.neutron-star-interiors.cw-mountains",
      "fields": {
        "precise": {
          "text": "Searches for continuous gravitational waves from known pulsars set upper limits on ellipticity $\\epsilon$ of order $10^{-8}\\ \\text{to}\\ 10^{-9}$ for some nearby millisecond pulsars. Determine the maximum ellipticity a realistic crust can sustain (estimates range from about $10^{-9}\\ \\text{to}\\ 10^{-6}$ depending on how the mountain is built) and whether a floor near $\\epsilon \\sim 10^{-9}$ exists, as suggested by millisecond-pulsar spin-down.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A detection of continuous gravitational waves, or a crust-elasticity calculation with a self-consistent formation history giving $\\epsilon_{\\max}$ below current limits.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.neutron-star-interiors.glitch-trigger",
      "fields": {
        "precise": {
          "text": "Glitches have fractional spin-up $\\Delta \\nu/\\nu \\sim 10^{-11} \\text{ to } 10^{-5}$, with power-law size distributions in most pulsars and quasi-periodic large events ($\\Delta \\nu/\\nu \\sim 10^{-6}$, about every 3 yr) in Vela. Determine the trigger: collective unpinning avalanches of superfluid vortices, crust quakes, or hydrodynamic instabilities of the superfluid-crust counterflow, and derive the observed size and waiting-time statistics and the sub-minute spin-up timescale.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.neutron-star-interiors.r-mode-instability",
      "fields": {
        "precise": {
          "text": "With standard shear and bulk viscosity, low-mass X-ray binaries spinning at $300\\ \\text{to}\\ 700\\ \\mathrm{Hz}$ with inferred core temperatures of about $10^{8}\\ \\mathrm{K}$ lie inside the r-mode instability window. Determine the extra damping (viscous crust-core boundary layer, hyperon or quark bulk viscosity, superfluid mutual friction, resonances) or the low saturation amplitude that reconciles theory with the observed spin and temperature distribution.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.protoplanetary-disks.dust-rings",
      "fields": {
        "precise": {
          "text": "ALMA images show axisymmetric dust rings and gaps at $10\\text{-}100\\,\\mathrm{AU}$ in $\\sim 1\\,\\mathrm{Myr}$ disks. Determine for the population whether gaps are opened by embedded planets of $\\sim 0.1-1\\ \\text{Jupiter masses}$ or by non-planetary processes (condensation fronts, magnetohydrodynamic zonal flows, secular gravitational instability). The answer is the fraction of gaps with a planetary origin.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.coherent-radio-mechanism",
      "fields": {
        "precise": {
          "text": "Pulsar radio brightness temperatures exceed $10^{25}\\,\\mathrm{K}$. Identify the mechanism (plasma instabilities in the outflow, coherent curvature radiation from charge bunches, direct emission from nonstationary pair discharges) that reproduces the mean spectrum (flux ~ nu^-1.6), radius-to-frequency mapping, polarization and the population of luminosities. Answer: a first-principles kinetic model reproducing these observables.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.flare-trigger",
      "fields": {
        "plain": {
          "text": "Magnetars sometimes release up to about $10^{46}\\,\\mathrm{erg}$ in a fraction of a second, possibly when their solid crust cracks under magnetic stress or when twisted magnetic field outside the star suddenly reconnects.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Giant flares (SGR 0526-66 in 1979, SGR 1900+14 in 1998, SGR 1806-20 in 2004 with $E \\sim 2 \\times 10^{46}\\,\\mathrm{erg}$, and the extragalactic GRB 200415A) and short bursts ($10^{37} \\text{ to } 10^{41}\\,\\mathrm{erg}$) require a trigger. Decide between crustal failure (starquakes, plastic flow) and magnetospheric instability or reconnection of twisted fields, using millisecond rise times, quasi-periodic oscillations of $18 \\text{ to } 1800\\,\\mathrm{Hz}$ in flare tails, burst energy distributions, and associated timing changes (glitches and anti-glitches). Answer: the trigger with quantitative evidence.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.long-period-transients",
      "fields": {
        "precise": {
          "text": "Long-period radio transients (periods from $\\sim 1\\,\\min$ to several hours, for example GCRT J1745-3009 at $77\\,\\min$, GLEAM-X J1627-52 at $18\\,\\min$ and GPM J1839-10 at $21\\,\\min$) emit coherent, highly polarized pulses below conventional pulsar death lines. Two, ILT J1101+5521 and GLEAM-X J0704-37, are white dwarf-M dwarf binaries. Determine whether all are white-dwarf systems or whether some are ultra-long-period magnetars, and identify the emission mechanism. Answer: a classification per source with a mechanism consistent with spin-down or binary energy budgets.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.magnetar-field-origin",
      "fields": {
        "precise": {
          "text": "Determine whether magnetar dipole fields $B \\sim 10^{14}\\ \\text{to}\\ 10^{15}\\ \\mathrm{G}$ arise from flux conservation of fossil fields in magnetic massive stars (possibly stellar-merger products), from convective or magnetorotational dynamos in a proto-neutron star spinning at $P$ of a few ms, or from a fall-back-driven Tayler-Spruit dynamo. Answer: the channel or channels consistent with the magnetar birth fraction (estimates ~10 to 40 percent of neutron stars), ordinary supernova remnant energies and kick distributions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.pair-discharge-test",
      "fields": {
        "precise": {
          "text": "Using global 3D kinetic plasma simulations with quantum-electrodynamic pair production at realistic field strength ($B \\sim 10^{12}\\,\\mathrm{G}$) and scale separation, compute the radio luminosity, spectrum and polarization from polar-cap discharges and compare with population averages (spectral index $\\sim -1.6$, luminosity versus spin-down power). Answer: yes or no with a quantitative comparison.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.pulsars-magnetars.wind-sigma-problem",
      "fields": {
        "precise": {
          "text": "The magnetization $\\sigma$ (Poynting flux over particle energy flux) of a pulsar wind is $\\sim 10^{4}$ or more near the light cylinder, while one-dimensional models of the Crab nebula require $\\sigma \\sim 10^{-3}$ at the termination shock ($r \\sim 3 \\times 10^{17}\\,\\mathrm{cm}$), and ideal MHD acceleration of a radial wind is inefficient. Determine where and how the magnetic energy dissipates: reconnection in the striped-wind current sheet, at the termination shock, or inside the nebula through kink instabilities. Answer: the dissipation site and fraction consistent with nebular spectra, morphology and gamma-ray flares.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.r-process-sites.collapsar-yield",
      "fields": {
        "precise": {
          "text": "In GRMHD simulations of collapsar disks (accretion rates $10^{-3}\\text{ to }1\\,M_{\\mathrm{sun}}/\\mathrm{s}$) with neutrino transport, determine the electron-fraction $Y_{e}$ distribution of the outflows and the mass with $Y_{e} < 0.25$ needed for lanthanides and the third r-process peak. Answer: r-process yield per event in $M_{\\mathrm{sun}}$, with the dependence on neutrino-transport method quantified.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.r-process-sites.dominant-site",
      "fields": {
        "status_note": {
          "text": "2025: delayed MeV emission after the 2004 SGR 1806-20 giant flare was interpreted as radioactive decay of about $10^{-6}\\,M_{\\mathrm{sun}}$ of fresh r-process matter, adding magnetar flares as a minor site.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.radius-valley.magma-envelope-coupling",
      "fields": {
        "precise": {
          "text": "For sub-Neptunes with surface magma oceans at $T \\sim 2000-4000\\,\\mathrm{K}$ under $\\mathrm{H_2}$ envelopes of $\\sim 1-3\\,\\mathrm{percent}$ of the planet mass, determine how $\\mathrm{H_2}$ dissolution into silicate melt and reactions with the melt (FeO and $\\mathrm{SiO_2}$ reduction producing $\\mathrm{H_2O}$, SiO and $\\mathrm{SiH_4}$) set the envelope composition and its mean molecular weight $\\mu$. The answer is predicted $\\mu$ and $\\mathrm{H_2O}$, $\\mathrm{CO_2}$ and SiO abundances versus equilibrium temperature and envelope mass fraction, testable against JWST spectra.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.radius-valley.sub-neptune-composition",
      "fields": {
        "precise": {
          "text": "For planets with $R \\sim 2-3.5\\,R_{\\mathrm{earth}}$ and $M \\sim 5-15\\,M_{\\mathrm{earth}}$, determine the bulk composition: rocky cores with H/He envelopes of $\\sim 1-3\\%$ by mass, water mass fractions of $\\sim 10-50\\%$ in supercritical layers, or magma oceans that dissolve and mix with hydrogen. The answer is a classification of individual planets and the population fractions, using JWST transmission spectra (mean molecular weight, $\\mathrm{H_2O}$, $\\mathrm{CH_4}$, $\\mathrm{CO_2}$, $\\mathrm{NH_3}$ abundances) together with interior models.",
          "how": [
            "inside:percent",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.radius-valley.water-worlds",
      "fields": {
        "precise": {
          "text": "Determine whether any planet with $R \\sim 1.5-3.5\\ R_{\\mathrm{earth}}$ and $P < 100\\ \\mathrm{d}$ has a water mass fraction above 0.1, demonstrated by a combination of bulk density and an atmospheric mean molecular weight and $\\mathrm{H_2O}$ abundance that a rocky core with an H/He envelope or a magma-ocean model cannot reproduce. The answer is yes or no, with the planets and water fractions if yes.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "JWST spectra giving high mean molecular weight and $\\mathrm{H_2O}$-dominated composition for a planet whose mass and radius are measured to better than 10 and 3 percent, fitted with interior models that include supercritical water and hydrogen-water mixing.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.sn-ia-progenitors.magnetic-wd-origin",
      "fields": {
        "precise": {
          "text": "Volume-limited samples show the magnetic fraction of white dwarfs rising with cooling age, with fields from about $10^{3}$ to $10^{9}$ G. Determine which mechanism (fossil field from the progenitor, dynamo during a merger or common envelope, or a dynamo driven by compositional convection during core crystallization) accounts for the observed incidence versus age, mass and binarity and for the field-strength distribution, including the breakout time of a field generated deep in the core.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.sn-ia-progenitors.missing-companions",
      "fields": {
        "precise": {
          "text": "Single-degenerate models predict a surviving donor at the center of young SN Ia remnants (for example Tycho, Kepler, SN 1006, SNR 0509-67.5), inflated and overluminous for $10^{3} \\text{ to } 10^{4}\\,\\mathrm{yr}$ and moving at a few hundred km/s; deep HST searches exclude such stars in several remnants. Explain the nondetections (double-degenerate origin, spin-up/spin-down delay that lets the donor shrink, or misidentified models), and reconcile the observed hypervelocity white dwarfs moving above $1000\\,\\mathrm{km/s}$ with the number expected if double detonations eject surviving companions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-corona-wind.coronal-heating",
      "fields": {
        "title": {
          "text": "What heats the solar corona above $10^{6}\\ \\mathrm{K}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "The quiet corona requires an energy flux of $\\sim 3 \\times 10^{5}\\ \\mathrm{erg}\\ \\mathrm{cm}^{-2}\\ \\mathrm{s}^{-1}$ and active regions $\\sim 10^{7}\\ \\mathrm{erg}\\ \\mathrm{cm}^{-2}\\ \\mathrm{s}^{-1}$. Determine the dominant dissipation mechanism: Alfven-wave turbulence, resonant absorption and phase mixing of waves, or nanoflares (small reconnection events) in braided fields. Answer: mechanisms with energy fluxes matching these requirements, by region type.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-corona-wind.fast-wind-energy",
      "fields": {
        "plain": {
          "text": "The fast solar wind leaves the Sun at about $7.5 \\times 10^{7}\\,\\mathrm{cm/s}$, and it is not settled whether waves in the magnetic field or bursts of magnetic reconnection push it to that speed.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Determine whether Alfven-wave turbulence, interchange reconnection at the base of coronal holes, or both supply the energy and momentum flux of the fast wind (speed $\\sim 7 \\times 10^{7}\\ \\text{to}\\ 8 \\times 10^{7}\\,\\mathrm{cm}/\\mathrm{s}$), including the heating of protons and heavy ions above the electron temperature. Answer: the fraction of the energy flux supplied by each process, consistent with Parker Solar Probe and Solar Orbiter data inside and near the Alfven surface.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-corona-wind.nanoflare-vs-wave",
      "fields": {
        "precise": {
          "text": "For active-region loops at $T \\sim 10^{6}\\ \\text{to}\\ 5 \\times 10^{6}\\,\\mathrm{K}$, determine the fraction of heating delivered impulsively (nanoflares with repeat times longer than the cooling time, producing faint plasma at $5 \\times 10^{6}\\ \\text{to}\\ 10^{7}\\,\\mathrm{K}$) versus steadily. Observables: slope of the emission measure distribution $\\mathrm{EM}(T) \\sim T^a$ below the peak and the hot emission measure above $5 \\times 10^{6}\\,\\mathrm{K}$. Answer: the impulsive fraction with uncertainty.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Spectroscopic measurement of faint $5 \\times 10^{6}\\ \\text{to}\\ 10^{7}\\,\\mathrm{K}$ emission in active regions compared with forward models of both heating types.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-corona-wind.slow-wind-source",
      "fields": {
        "precise": {
          "text": "Determine the fractional contributions to the slow wind ($3 \\times 10^{7}\\text{ to }5 \\times 10^{7}\\,\\mathrm{cm}/\\mathrm{s}$) of (i) open fields at coronal-hole boundaries with large expansion factors, (ii) interchange reconnection releasing plasma from closed loops along the network of open-closed boundaries, and (iii) blobs from helmet-streamer tops. Use composition ($\\mathrm{O}7+/\\mathrm{O}6+$ ratio, $\\mathrm{Fe}/\\mathrm{O}$ enhancement of low-first-ionization-potential elements), Alfvenicity and magnetic connectivity mapping from Solar Orbiter and Parker Solar Probe. Answer: fractions with uncertainties.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-interior-cycle.abundance-problem",
      "fields": {
        "precise": {
          "text": "Standard solar models using 3D non-LTE photospheric abundances (Asplund et al. 2009 and 2021, $Z/X \\sim 0.018$) disagree with the helioseismic sound speed below the convection zone (deviations $\\sim 1\\%$), the convection-zone base $R_{\\mathrm{cz}} = 0.713\\,R_{\\mathrm{sun}}$ and surface helium $Y_{s} \\sim 0.248$, while higher-metallicity analyses (Magg et al. 2022, $Z/X = 0.0225$) restore much of the agreement. Determine the correct metal content and whether opacity revisions near $T \\sim 2 \\times 10^{6}\\,\\mathrm{K}$ or other physics are needed. Answer: $Z/X$ with uncertainty consistent with helioseismology and the CNO solar neutrino flux.",
          "how": [
            "inside:e-notation",
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.solar-interior-cycle.grand-minima",
      "fields": {
        "precise": {
          "text": "Cosmogenic isotope records (C-14, Be-10) show a few tens of grand minima over the last $\\sim 10^{4}\\,\\mathrm{yr}$, occupying of order one sixth of the time. Determine whether entry and exit arise from stochastic fluctuations in the Babcock-Leighton poloidal source (scatter of active-region tilt angles, rare anomalous active regions), from nonlinear deterministic dynamo dynamics, or from changes in meridional flow, and whether the waiting-time distribution is exponential. Answer: a model reproducing the frequency and duration distribution of grand minima and the hemispheric asymmetry of the Maunder Minimum.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.star-cluster-formation.emsto-rotation",
      "fields": {
        "precise": {
          "text": "Intermediate-age and young clusters in the Magellanic Clouds and the Milky Way show extended main-sequence turnoffs and split main sequences (first reported for NGC 1846, Mackey and Broby Nielsen 2007), attributed mainly to a spread in stellar rotation rather than an age spread. Determine the origin of the bimodal rotation distribution (initial conditions set during star formation, tidal braking in binaries, or mergers producing slow rotators) and whether any residual age spread of order $10^{8}\\,\\mathrm{yr}$ is required.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.star-formation-imf.low-efficiency",
      "fields": {
        "precise": {
          "text": "Molecular clouds convert gas into stars at efficiency per free-fall time eps_ff = SFR t_ff / M_gas ~ 0.01, with integrated cloud efficiencies of $\\sim 1-10\\%$ before dispersal. Explain the value and its scatter as a function of cloud surface density and virial parameter, separating the roles of supersonic turbulence, magnetic support and stellar feedback (photoionization, winds, radiation pressure, jets, supernovae).",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.stellar-mixing.red-giant-core-rotation",
      "fields": {
        "precise": {
          "text": "Asteroseismic rotational splittings of mixed modes give core rotation rates of low-mass subgiants and red giants roughly 10 to 100 times below those of models with hydrodynamic transport and also below models with the Tayler-Spruit magnetic dynamo. Identify the angular momentum transport process (magnetic instabilities, internal gravity waves, mixed-mode transport, or another) and its effective viscosity $\\nu_{\\mathrm{AM}} \\sim 10^{3} \\text{ to } 10^{5}\\,\\mathrm{cm}^{2}/\\mathrm{s}$ required, as a function of mass and evolutionary stage, so that models reproduce the measured core and envelope rates.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.system-architectures.super-earth-cold-jupiter",
      "fields": {
        "precise": {
          "text": "Measure $P(\\mathrm{CJ}\\mid \\mathrm{SE})$, the occurrence of cold Jupiters ($M\\,\\mathrm{sin}\\,i \\sim 0.3-13\\ M_{\\mathrm{Jup}}, a \\sim 1-10\\ \\mathrm{AU}$) around hosts of inner super-Earths ($R = 1-4\\,R_{\\mathrm{earth}}, P < 100\\,\\mathrm{d}$), versus the field rate of about 10 percent. Zhu and Wu 2018 and Bryan et al. 2019 ($39 \\pm 7\\%$) report an excess of about three times, while Bonomo et al. 2023 (A&A 677, A33) find $9.3(+7.7,-2.9)\\%$ and no excess. The answer is $P(\\mathrm{CJ}\\mid \\mathrm{SE})$ with metallicity dependence and uncertainty sufficient to decide the excess.",
          "how": [
            "inside:percent",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.tidal-disruption-events.missing-energy",
      "fields": {
        "precise": {
          "text": "Accreting about $0.5\\,M_{\\mathrm{sun}}$ with radiative efficiency 0.1 releases of order $10^{53}$ erg, while observed optical and UV TDEs radiate about $10^{50}$ to $10^{51}$ erg. Determine where the remainder goes: extreme-UV emission, slow accretion over years, kinetic energy of outflows, advection into the black hole, or a smaller accreted mass.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "astro.tidal-disruption-events.optical-emission",
      "fields": {
        "precise": {
          "text": "Optical and UV emission of TDEs is roughly blackbody with $T \\sim 2 \\times 10^{4} \\text{ to } 4 \\times 10^{4}\\,\\mathrm{K}$ and $\\mathrm{radius} \\sim 10^{14} \\text{ to } 10^{15}\\,\\mathrm{cm}$, much larger than the circularization radius. Determine whether it is powered by shocks where the debris stream intersects itself (Piran et al. 2015) or by reprocessing of accretion luminosity in an optically thick envelope or outflow, using light-curve shapes, line profiles and X-ray to optical ratios.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.advanced-structures.dielectric-gv-breakdown",
      "fields": {
        "precise": {
          "text": "Fused-silica and diamond structures driven by sub-picosecond electron bunches ($\\sigma_z$ $\\sim 2 \\times 10^{-3}$ to $10^{-2}$ cm) sustained surface fields of order $eE \\sim 100\\ \\mathrm{MeV}/\\mathrm{cm}$ before damage (SLAC experiments from 2008 onward). Determine the damage mechanism and its scaling with field duration from 0.1 to 10 ps and with band gap, separating field-induced ionization, heating by beam halo, and surface charging.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.advanced-structures.dla-relativistic-scaleup",
      "fields": {
        "title": {
          "text": "Can dielectric laser accelerators reach staged MeV gain with useful charge?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Dielectric laser accelerators with alternating-phase focusing have shown coherent acceleration and transport of sub-relativistic electrons over sub-millimeter lengths (2021-2023), and single unstaged gratings driven by pulse-front-tilted lasers have given energy modulation up to $\\sim 0.5\\,\\mathrm{MeV}$ for relativistic electrons (UCLA, 2024-2025). Determine whether a staged DLA can deliver net energy gain above $1\\,\\mathrm{MeV}$ with transverse and longitudinal confinement and at least $10^{4}$ electrons per optical microbunch train, given apertures of order the laser wavelength ($\\sim 10^{-4}\\,\\mathrm{cm}$), wakefields, space charge and laser damage.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-beam-limit.crab-waist-instability",
      "fields": {
        "precise": {
          "text": "In crab-waist schemes with Piwinski angle $\\phi >> 1$, strong-strong simulations predict coherent X-Z instabilities and interplay with longitudinal and transverse impedance. Determine the stability boundary in $(\\xi_x,\\xi_y,\\nu_s,\\mathrm{impedance})$ and whether it explains the luminosity shortfall of SuperKEKB relative to its design value of $8 \\times 10^{35}\\ \\mathrm{cm}^{-2}\\ \\mathrm{s}^{-1}$ (later target about $6.5 \\times 10^{35}$).",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "SuperKEKB set a world-record peak of about $5.1 \\times 10^{34}\\,\\mathrm{cm}^{-2}\\,\\mathrm{s}^{-1}$ in December 2024, roughly 6 to 8 percent of its design and later target values; vertical blow-up, a vertical instability linked to collimator impedance and sudden beam losses are the identified limits.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-beam-limit.hadron-diffusion",
      "fields": {
        "title": {
          "text": "What sets the much lower beam-beam limit in hadron colliders?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Without radiation damping, hadron colliders are limited to total $\\xi \\sim 0.01\\ \\text{to}\\ 0.03$. Predict the beam lifetime and emittance growth over $10^{8}$ to $10^{9}$ turns from beam-beam nonlinearities combined with tune modulation, power-supply ripple and noise, and determine the scaling of the limit with these noise sources.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-brightness.minimum-photocathode-mte",
      "fields": {
        "precise": {
          "text": "The intrinsic normalized emittance of a photoemission source is eps_n = $\\sigma_x$ sqrt(MTE/(m c^2)), with sigma_x the rms source size and MTE the mean transverse energy of emitted electrons. Values of approximately $5\\,\\mathrm{meV}$ were reported around 2020 from near-threshold photoemission of cryogenically cooled single-crystal Cu(100). Determine the lowest achievable MTE at quantum efficiency $\\ge 10^{-5}$ and the physics that sets it (lattice temperature, surface roughness and work-function variation, electron-phonon and electron-electron scattering, multiphoton emission).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-brightness.photoinjector-brightness-limit",
      "fields": {
        "title": {
          "text": "Can photoinjectors reach the space-charge-limited brightness bound?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-brightness.ring-ultimate-emittance",
      "fields": {
        "precise": {
          "text": "Multibend-achromat rings at $6\\,\\mathrm{GeV}$ operate with natural horizontal emittance eps_x of about $1.3 \\times 10^{-8}$ to $1.4 \\times 10^{-8}$ cm rad (ESRF-EBS, from 2020) and about $4 \\times 10^{-9}$ cm rad (APS-U, from 2024). Determine the minimal equilibrium eps_x at $E = 6\\,\\mathrm{GeV}$ and circumference $10^{5}-2 \\times 10^{5}\\,\\mathrm{cm}$ with intrabeam scattering at full current, Touschek lifetime above $1\\,\\mathrm{h}$, and dynamic aperture adequate for on-axis or off-axis injection, and whether eps_x < $10^{-9}$ cm rad (diffraction limit for $\\sim 10\\,\\mathrm{keV}$ photons) is attainable.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-cooling.muon-6d-final-cooling",
      "fields": {
        "precise": {
          "text": "Transverse ionization cooling of muons through a single absorber was demonstrated by MICE (published 2020). Determine whether a realistic 6D cooling channel plus final cooling stage can reach normalized transverse emittance of approximately $2.5 \\times 10^{-3}$ cm and longitudinal emittance of approximately $7\\,\\mathrm{cm}$ with overall muon transmission above $\\sim 10$ percent, including RF limits in solenoid fields, absorber heating, space charge and muon decay.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.beam-cooling.osc-high-energy",
      "fields": {
        "precise": {
          "text": "Optical stochastic cooling was demonstrated with $100\\,\\mathrm{MeV}$ electrons at the Fermilab IOTA ring (published 2022) using undulator light at $\\sim 10^{-4}\\,\\mathrm{cm}$ wavelength without optical amplification. Determine whether OSC with optical amplification can cool protons at $100\\,\\mathrm{GeV} \\text{ to } 7\\,\\mathrm{TeV}$ with damping time shorter than the intrabeam-scattering time, given undulator radiation per proton, amplifier gain and bandwidth, and path-length stability of $\\sim 0.1$ wavelength.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.collective-instabilities.beam-beam-limit",
      "fields": {
        "title": {
          "text": "What sets the beam-beam tune-shift limit in electron-positron colliders?",
          "how": [
            "title:question-mark"
          ]
        },
        "settled_by": {
          "text": "A theory or strong-strong simulation predicting $\\xi_y,\\mathrm{max}$ for the three colliders within 20 percent with one set of assumptions.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.collective-instabilities.dust-release-mechanism",
      "fields": {
        "precise": {
          "text": "Fast loss events in the LHC (called UFOs, unidentified falling objects) last of order $10^{-3}$ s and are modeled as micron-scale dust grains entering the proton beam, being ionized and repelled; this dust-beam dynamics was analyzed in 2020. Determine the release mechanism (electrostatic detachment driven by beam-induced charging or electron cloud, mechanical vibration, magnetic forces on ferromagnetic grains) and predict the event rate versus beam intensity, bunch spacing and cumulative beam time.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.csr-microbunching.3d-csr-emittance-growth",
      "fields": {
        "precise": {
          "text": "The 1D steady-state CSR wake for a bunch of rms length $\\sigma_z$ on a bend of radius $R$ is valid when the transverse size satisfies $\\sigma_x << (\\sigma_z^2 R)^{1/3}$. For magnetic bunch compressors where this inequality fails ($\\sigma_z \\sim 10^{-4}$ to $10^{-3}$ cm, $10^{8}$ to $10^{10}$ electrons per bunch), compute projected and slice emittance growth including the transverse variation of the radiation field, transient fields at magnet entrance and exit, and vacuum-chamber shielding, and state the parameter region in which the 1D model errs by more than a factor 2.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.csr-microbunching.ring-csr-instability-threshold",
      "fields": {
        "precise": {
          "text": "For a Gaussian bunch in an electron ring with the shielded steady-state CSR impedance, Vlasov-Fokker-Planck calculations give a threshold in the dimensionless current $S_{\\mathrm{csr}}$ of approximately $S_{\\mathrm{csr}},\\mathrm{th} = 0.5 + 0.12$ $\\Pi$, with $\\Pi$ the shielding parameter, plus a narrow low-threshold region near $\\Pi \\sim 0.7$ (2010). Determine whether the threshold and the period and amplitude of sawtooth bursting above it are predicted within 20 percent once the full ring impedance, potential-well distortion and finite chamber geometry are included, in low-momentum-compaction operation of several rings.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.csr-microbunching.ssmb-euv-source",
      "fields": {
        "precise": {
          "text": "Steady-state microbunching (SSMB) uses laser modulators for longitudinal focusing in a low-momentum-compaction ring so that electrons stay in optical-scale microbunches turn after turn; retention of laser-induced microbunching at a $1.064 \\times 10^{-4}\\,\\mathrm{cm}$ wavelength over successive turns was reported at the Metrology Light Source, Berlin, in 2021 (Deng et al., https://doi.org/10.1038/s41586-021-03203-0). Determine whether a ring can hold microbunches of rms length below $\\sim 2 \\times 10^{-7}\\,\\mathrm{cm}$ in steady state, with quantum excitation, intrabeam scattering and laser phase noise included, giving coherent radiation at $1.35 \\times 10^{-6}\\,\\mathrm{cm}$ ($13.5\\,\\mathrm{nm}$) with average power near $10^{10}\\,\\mathrm{erg}/\\mathrm{s}$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.fel-physics.eehg-harmonic-limit",
      "fields": {
        "precise": {
          "text": "In echo-enabled harmonic generation (EEHG), two laser modulators and two dispersive chicanes produce density bunching at harmonic $h$ of a seed laser of wavelength $\\sim 2.6 \\times 10^{-5}\\,\\mathrm{cm}$. Determine the maximal $h$ at which EEHG gives bunching well above shot noise and lasing with near-transform-limited spectra, including intrabeam scattering and incoherent synchrotron radiation in the strong chicane, coherent synchrotron radiation, and seed-laser phase noise, and whether wavelengths near $10^{-7}\\,\\mathrm{cm}$ are reachable.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.fel-physics.shortest-sase-wavelength",
      "fields": {
        "precise": {
          "text": "For a SASE FEL with electron energy $\\gamma m c^2$, normalized emittance eps_n, slice energy spread $\\sigma_E$, undulator period $\\lambda_u$ and parameter $K$, quantum diffusion from incoherent undulator radiation grows $\\sigma_E^2$ at a rate $\\sim \\gamma^4 K^2 F(K)/\\lambda_u^3$. Find the minimal resonant wavelength at which saturation is reachable for eps_n >= $10^{-5}$ cm and realistic undulator technology, and whether lasing at photon energies above $100\\,\\mathrm{keV}$ is possible.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.fel-physics.shot-noise-suppression",
      "fields": {
        "precise": {
          "text": "Coulomb repulsion acting over a quarter plasma period in a drift can reduce beam density fluctuations below the Poisson shot-noise level. Determine whether suppression by more than 10 dB can be produced and kept through acceleration and compression at wavelengths below $10^{-5}$ cm, which would reduce SASE start-up noise and microbunching gain.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.fel-physics.slice-energy-spread",
      "fields": {
        "title": {
          "text": "What sets the uncorrelated energy spread of high-brightness electron beams?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In photoinjectors with $10^{8}\\ \\text{to}\\ 10^{9}$ electrons per bunch, determine the contributions of intrabeam scattering, shot-noise-seeded microbunching instability and cathode emission to the slice energy spread $\\sigma_E$ (few keV) at injector exit and after bunch compression, and predict $\\sigma_E$ within $20\\%$ of measured values at several facilities.",
          "how": [
            "inside:e-notation",
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.fel-physics.xfelo-gain",
      "fields": {
        "precise": {
          "text": "In an x-ray FEL oscillator, hard x-ray pulses of photon energy $\\sim 5\\text{-}15\\ \\mathrm{keV}$ circulate in a Bragg-crystal cavity with round-trip reflectivity above $\\sim 85\\%$ and are amplified by successive electron bunches synchronized with the round trip. Determine experimentally whether round-trip gain exceeding total cavity loss, sustained exponential growth over many passes, and saturation with relative bandwidth $\\sim 10^{-7}$ can be obtained with existing high-repetition-rate linac beams, given crystal heat load and cavity alignment stability.",
          "how": [
            "inside:e-notation",
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.microbunching-fel.transform-limited",
      "fields": {
        "title": {
          "text": "Can XFELs produce stable transform-limited hard X-ray pulses?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.muon-ionization-cooling.collective-effects",
      "fields": {
        "precise": {
          "text": "For bunches of $N \\sim 4 \\times 10^{12}$ muons passing low-$Z$ absorbers (LiH, liquid $\\mathrm{H_2}$, $\\mathrm{H_2}$ gas) in a 6D cooling lattice, quantify emittance growth from space charge, wakefields and the ionization plasma created in the absorber, and determine whether they limit cooling at the design intensity.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.muon-ionization-cooling.final-emittance",
      "fields": {
        "title": {
          "text": "Can final cooling reach collider transverse emittance with acceptable longitudinal growth?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Muon collider design studies (MAP, the US Muon Accelerator Program, then IMCC, the International Muon Collider Collaboration) set normalized emittance targets of about eps_T ~ 22.5 to 25 micron transverse and eps_L ~ 70 mm (7.5 MeV m) longitudinal at the end of cooling. Determine whether a final-cooling channel using very high field solenoids ($B \\sim 300 \\text{ to } 400\\,\\mathrm{kG}$) or thick wedge absorbers reaches eps_T <= 25 micron with eps_L <= 75 mm and muon transmission above $\\sim 50\\%$, including decay losses.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nb3sn-cavities.exceed-nb",
      "fields": {
        "title": {
          "text": "Can a $\\mathrm{Nb_3Sn}$ cavity exceed the gradient of the best niobium cavities?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "The goal of $\\mathrm{Nb_3Sn}$ is to go beyond niobium, but so far niobium still holds the gradient record. The question is whether any $\\mathrm{Nb_3Sn}$ cavity can beat it.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether a $\\mathrm{Nb_3Sn}$-coated 1.3 GHz elliptical cavity can sustain $E_{\\mathrm{acc}}>0.45\\,\\mathrm{MV}/\\mathrm{cm}$ ($B_{\\mathrm{pk}}>1900\\,\\mathrm{G}$) at any temperature with $Q_{0}>10^{10}$, or whether intrinsic film properties (grain boundaries, thin-film thermal limits) forbid it.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "A $\\mathrm{Nb_3Sn}$ cavity test exceeding the Nb record gradient, or a demonstrated intrinsic bound below it.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nb3sn-cavities.q-slope",
      "fields": {
        "title": {
          "text": "Origin of the field-dependent losses in $\\mathrm{Nb_3Sn}$ cavities",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Even before stopping, $\\mathrm{Nb_3Sn}$ cavities lose more energy as the field grows. The source of this extra loss is unclear.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "$\\mathrm{Nb_3Sn}$ cavities at 4.2 K and 1.3 GHz show $Q_{0}$ decreasing with $B_{\\mathrm{pk}}$ above $\\sim 300\\ \\text{to}\\ 500\\,\\mathrm{G}$. Determine whether this arises from grain-boundary Josephson weak links, vortex penetration at local defects, tin-poor phases, or nonlinear BCS response, with a model predicting $Q_{0}(B_{\\mathrm{pk}}, T)$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nonlinear-dynamics.diffusion-rate-4d-maps",
      "fields": {
        "precise": {
          "text": "For a 4D symplectic map of linear rotation with tunes $(Q_x, Q_y)$ plus thin sextupole and octupole kicks of strength $\\epsilon$, with tune modulation $\\Delta Q \\sim 10^{-5} \\text{ to } 10^{-4}$ at frequencies $50\\,\\mathrm{Hz} \\text{ to } 10\\,\\mathrm{kHz}$ from power-supply ripple, compute the rate of chaotic transport in action (Arnold and modulational diffusion) at amplitudes below the short-term dynamic aperture as a function of $\\epsilon$ and $\\Delta Q$. Test against direct tracking to $10^{9}$ turns.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nonlinear-dynamics.early-chaos-indicators",
      "fields": {
        "title": {
          "text": "Do short-time chaos indicators predict long-term orbit stability?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For realistic hadron collider maps, determine whether indicators computed over $10^{3}$ to $10^{4}$ turns (frequency-map diffusion, finite-time Lyapunov exponents, reversibility error, or machine-learned combinations) classify initial conditions stable for $10^{6}$ to $10^{8}$ turns with misclassification below 1 percent, and identify where in amplitude space they fail.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nonlinear-dynamics.integrable-lattice-tolerance",
      "fields": {
        "precise": {
          "text": "Danilov-Nagaitsev nonlinear integrable optics keeps two invariants of transverse motion for a special elliptic potential inserted in a drift whose outside lattice acts as a phase-advance-pi lens. Determine the tune spread and dynamic aperture that survive relative magnet errors of $10^{-4}$, chromaticity, and synchrotron motion with energy spread $10^{-3}$, and compare with measurements of amplitude-dependent tune shift at IOTA.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.nonlinear-dynamics.long-term-da-scaling",
      "fields": {
        "precise": {
          "text": "The dynamic aperture $D(N)$, the largest initial amplitude stable for $N$ turns of the 4D or 6D symplectic one-turn map of a hadron collider, is fitted by Nekhoroshev-type laws $D(N) = D_{\\infty} + b/(\\mathrm{log}\\, N)^{\\kappa}$. Determine whether such a law fitted for $N \\le 10^{6}$ predicts $D(N)$ and the resulting intensity decay at $N \\sim 10^{9}$ (about $10^{5}$ s of LHC operation) to within 10 percent, and derive $\\kappa$ from the resonance structure of the map.",
          "how": [
            "inside:e-notation",
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Direct tracking to $10^{9}$ turns of a realistic lattice compared with the extrapolation, plus a derivation of $\\kappa$ from normal-form or resonance analysis.",
          "how": [
            "outside:e-notation"
          ]
        },
        "status_note": {
          "text": "Fitted scaling laws described LHC intensity and luminosity evolution in several fills (2018-2019 papers); a derivation of the exponent and a test at $10^{9}$ turns are missing.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.photocathode-emittance.mte-qe-tradeoff",
      "fields": {
        "settled_by": {
          "text": "A derived bound $\\mathrm{MTE}_{\\min}(\\mathrm{QE})$ from photoemission theory checked against measurements on candidate materials.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.photocathode-emittance.subthermal-mte",
      "fields": {
        "title": {
          "text": "Is a mean transverse energy below the thermal value achievable and usable?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For near-threshold photoemission the mean transverse energy is usually bounded below by $\\mathrm{MTE} \\sim k_{\\mathrm{B}} T$ of the electron distribution. Determine whether mechanisms such as refraction at an effective-mass discontinuity at the surface or band-structure selection give $\\mathrm{MTE} < k_{\\mathrm{B}} T$ at useful quantum efficiency ($\\mathrm{QE} > 10^{-5}$), and the minimum attainable MTE for a given material at $T = 300\\,\\mathrm{K}$.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.polarized-beams.edm-ring-systematics",
      "fields": {
        "precise": {
          "text": "In a frozen-spin all-electric ring for protons at the magic momentum $0.7007\\,\\mathrm{GeV}/c$, an EDM d rotates the spin vertically, with target sensitivity $d \\sim 10^{-29}\\,e\\,\\mathrm{cm}$. Determine whether counter-rotating beams and field reversals suppress spurious vertical spin rotation from radial magnetic fields, geometric phases of misaligned elements and vertical velocity to below the EDM signal at achievable alignment tolerances, with spin coherence time above $10^{3}\\,\\mathrm{s}$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.polarized-beams.fccee-energy-calibration",
      "fields": {
        "precise": {
          "text": "Resonant depolarization gives the beam energy to below $10^{-6}$ relative precision if a transverse polarization of about 5-10 percent builds up by the Sokolov-Ternov effect. For a $\\sim 9 \\times 10^{6}\\, \\mathrm{cm}$ circumference ring at $E = 45.6\\, \\mathrm{GeV}$ and $E \\sim 80\\, \\mathrm{GeV}$, determine the equilibrium polarization and build-up time with polarization wigglers, including depolarization from energy spread $\\sigma_E/E \\sim 4 \\times 10^{-4} \\text{ to } 10^{-3}$ and lattice errors, and whether calibration at the WW threshold is feasible.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.polarized-beams.snake-polarization-loss",
      "fields": {
        "precise": {
          "text": "RHIC accelerates polarized protons to $255\\,\\mathrm{GeV}$ with two full Siberian snakes, losing part of the injected polarization during acceleration through intrinsic and imperfection spin resonances. Determine the mechanism of the residual loss (higher-order snake resonances, overlap of intrinsic and imperfection resonances, spin-tune spread) and predict whether $N_s$ snakes preserve more than $70\\%$ polarization up to $275\\,\\mathrm{GeV}$ in an electron-ion collider hadron ring.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.polarized-beams.spin-coherence-time",
      "fields": {
        "precise": {
          "text": "Spin decoherence in a ring arises from the spread of spin tune driven by momentum spread and betatron amplitudes. Determine the maximal spin coherence time for protons and deuterons with chromatic sextupole correction and electron cooling, including space charge and intrabeam scattering, relative to the approximately $10^{3}\\,\\mathrm{s}$ reached for deuterons at the COSY ring (reported 2016).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.rf-breakdown.bdr-field-scaling",
      "fields": {
        "precise": {
          "text": "Measured breakdown rate per pulse per unit length in conditioned Cu structures follows $\\mathrm{BDR} \\sim E^{n} \\tau_{p}^{m}$ with n approximately 30 and m approximately 5 (CLIC test-stand data), and BDR at fixed field decreases slowly with accumulated pulse number (conditioning). Derive n, m and the conditioning curve from a microscopic model, and state whether the power law persists at BDR below $10^{-7}$ per pulse per meter of structure.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.rf-breakdown.local-field-criterion",
      "fields": {
        "title": {
          "text": "Which local field quantity determines the breakdown-limited gradient?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.rf-breakdown.magnetic-field-breakdown",
      "fields": {
        "precise": {
          "text": "Vacuum normal-conducting cavities at $\\sim 200\\text{-}800\\,\\mathrm{MHz}$ in axial magnetic fields $B \\sim 3 \\times 10^{4}\\,\\mathrm{G}$ show reduced maximum gradient, attributed to field-emitted electrons focused by B onto the walls, causing local heating. Establish the scaling of the safe gradient with B, frequency and wall material up to $B \\sim 10^{5}\\,\\mathrm{G}$ and above, as required for 6D muon ionization cooling channels.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "Beryllium-walled and high-pressure gas-filled cavities reached approximately $0.5\\,\\mathrm{MeV}/\\mathrm{cm}$ in fields near $3 \\times 10^{4}\\,\\mathrm{G}$ at the Fermilab MuCool Test Area (reported around 2020); higher fields remain untested.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.sc-magnets.hts-screening-currents",
      "fields": {
        "precise": {
          "text": "In REBCO coated-conductor coils (tape width $\\sim 0.4\\,\\mathrm{cm}$), screening currents induced during field ramps produce field harmonics and slow drifts well above the $10^{-4}$ relative field quality needed for beam optics, and add mechanical stress. Determine whether conductor layout (striated tapes, round twisted-tape cables) and ramp protocols can reduce screening-current field errors below $10^{-4}$ at fields $10^{5}\\ \\text{to}\\ 2 \\times 10^{5}\\,\\mathrm{G}$, and predict their decay in time from flux-creep parameters of the tape.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.sc-magnets.stress-degradation-limit",
      "fields": {
        "title": {
          "text": "Transverse-stress limit for irreversible degradation of $\\mathrm{Nb_3Sn}$ cables",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{Nb_3Sn}$ is brittle, and the huge magnetic forces in a high-field magnet squeeze the cable until its ability to carry current is permanently damaged; where that threshold lies and what breaks first is uncertain.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Rutherford cables of $\\mathrm{Nb_3Sn}$ filaments in epoxy-impregnated coils at fields up to $\\sim 1.6 \\times 10^{5}\\,\\mathrm{G}$ are under transverse stress of order $1.5 \\times 10^{9} \\text{ to } 2 \\times 10^{9}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$ (approximate). Determine the stress at which the critical current degrades irreversibly, its dependence on filament layout, impregnation and temperature cycling, and the microscopic failure mode (filament cracking, void collapse, debonding), as a function that fixes the maximal practical dipole field.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.sc-magnets.training-mechanism",
      "fields": {
        "title": {
          "text": "Microscopic origin of quench training in $\\mathrm{Nb_3Sn}$ accelerator magnets",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "$\\mathrm{Nb_3Sn}$ dipoles and quadrupoles operating at $1.1 \\times 10^{5}$ to $1.5 \\times 10^{5}$ G often require tens of training quenches to approach 80 to 90 percent of the conductor short-sample limit. Identify the energy-release events that start training quenches (epoxy cracking, conductor-insulation debonding, stick-slip friction at coil-structure interfaces), their energy spectrum relative to the minimum quench energy of the cable, and a model that predicts the training curve from coil prestress and material properties.",
          "how": [
            "outside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.space-charge-halo.electron-lens-compensation",
      "fields": {
        "title": {
          "text": "Can electron lenses compensate space charge in hadron rings?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.space-charge-halo.halo-loss-prediction",
      "fields": {
        "precise": {
          "text": "In MW-class proton and H- linacs (SNS, J-PARC, ESS, PIP-II) losses must stay below about $10^{-6}$ to $10^{-4}$ of the beam per unit length. Predict, blind and to within a factor 2, the halo population beyond 5 rms beam sizes from the measured initial distribution, lattice errors and space charge, and identify which mechanisms (envelope mismatch, particle-core resonances, intrabeam stripping of H- ions) dominate the measured loss pattern.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.space-charge-halo.integrable-optics-intensity",
      "fields": {
        "title": {
          "text": "Does nonlinear integrable optics raise the space-charge limit?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.space-charge-halo.max-tune-shift-ring",
      "fields": {
        "precise": {
          "text": "High-intensity synchrotrons operate with incoherent space-charge tune shift $\\left|\\Delta Q_{\\mathrm{sc}}\\right|$ up to approximately 0.2-0.5 over storage times of $10^{3}$ to $10^{5}$ turns. Derive, from the resonance structure of a given lattice and the periodic resonance crossing caused by synchrotron motion in a bunched beam, the maximal $\\left|\\Delta Q_{\\mathrm{sc}}\\right|$ compatible with emittance growth below 10 percent and loss below $10^{-3}$ over $N$ turns, and compare with CERN PS and SPS, J-PARC and GSI SIS18 data.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.srf-cavities.high-field-q-slope",
      "fields": {
        "precise": {
          "text": "Electropolished bulk Nb cavities at $1.3\\,\\mathrm{GHz}$ and $T = 2\\,\\mathrm{K}$ show a steep drop of quality factor $Q_0$ above peak surface magnetic field $H_{\\mathrm{pk}} \\sim 900-1000\\,\\mathrm{G}$, removed by in-situ baking at $120\\,\\mathrm{C}$ for $\\sim 48\\,\\mathrm{h}$. Identify the mechanism (niobium nanohydride precipitation within $\\sim 10^{-5}$ cm of the surface, oxygen or vacancy-hydrogen complexes, or other) with a model predicting the onset field and its dependence on bake temperature and duration.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.srf-cavities.nb3sn-early-quench",
      "fields": {
        "title": {
          "text": "Why $\\mathrm{Nb_3Sn}$ cavities quench far below their predicted field",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{Nb_3Sn}$ should hold about twice the field of niobium, but real cavities fail at roughly half of niobium's best.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Vapor-diffusion $\\mathrm{Nb_3Sn}$ films ($\\sim 2 \\times 10^{-4}\\,\\mathrm{cm}$ thick) on Nb cavities quench at $H_{\\mathrm{pk}} \\sim 800\\text{-}1200\\,\\mathrm{G}$, compared with a predicted $H_{\\mathrm{sh}}$ near $4000\\,\\mathrm{G}$. Identify the limiting mechanism (thin-grain regions, tin-depleted patches with low $H_c$, vortex entry at grain boundaries, thermal runaway in the low-conductivity film) and predict the quench field from measured film microstructure.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Single-cell $\\mathrm{Nb_3Sn}$ cavities reached accelerating gradients of approximately $0.24\\,\\mathrm{MeV}/\\mathrm{cm}$ by the early 2020s; the gap to the predicted superheating field remained.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.srf-cavities.residual-resistance-floor",
      "fields": {
        "title": {
          "text": "What sets the residual surface resistance floor of niobium cavities?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "At $T <\\sim 1.5\\,\\mathrm{K}$, where the BCS surface resistance at 1.3 GHz is negligible, the quality factor of the best Nb cavities saturates at $Q_0$ of order $10^{11}$ (residual resistance $\\sim 1-3\\,\\mathrm{nOhm}$), set by a temperature-independent residual surface resistance. Determine the fractions contributed by trapped magnetic vortices, two-level systems in the surface $\\mathrm{Nb_2O_5}$ oxide, and subgap quasiparticle states, as functions of field, frequency and surface treatment.",
          "how": [
            "outside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.srf-cavities.superheating-limit",
      "fields": {
        "title": {
          "text": "Can multilayer coatings raise the RF field above niobium's limit?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "The superheating field of clean Nb is $H_{\\mathrm{sh}}$ approximately 2000-2400 G at low T, and the best Nb cavities reach $H_{\\mathrm{pk}}$ near 2000 G. Determine whether superconductor-insulator-superconductor multilayers ($\\mathrm{Nb_3Sn}$, NbN or similar layers thinner than the London penetration depth on Nb) raise the attainable RF field above bulk Nb $H_{\\mathrm{sh}}$ in a cavity at $f \\sim 1\\, \\mathrm{GHz}$, and give the maximal field versus layer thickness and defect density.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.srf-cavities.thin-film-q-slope",
      "fields": {
        "precise": {
          "text": "Sputtered Nb films $\\sim 10^{-4} \\text{ to } 5 \\times 10^{-4}\\,\\mathrm{cm}$ thick on Cu cavities, as used at LEP, LHC and HIE-ISOLDE, show surface resistance $R_{\\mathrm{s}}$ rising roughly linearly with RF field from $H_{\\mathrm{pk}}$ of a few hundred G, unlike bulk Nb. Identify the mechanism (grain-boundary weak links and local hot spots, trapped flux in a granular film, poor film-substrate thermal contact, or other) and predict $R_{\\mathrm{s}}(H)$ from measured film microstructure for different deposition methods, including high-power impulse magnetron sputtering.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "beams.superheating-field.dynamic-hsh",
      "fields": {
        "precise": {
          "text": "Compute the dynamic superheating field $H_{\\mathrm{sh}}(f,T)$ for an s-wave superconductor driven at $f\\sim 0.1\\text{ to }10\\,\\mathrm{GHz}$, including nonequilibrium quasiparticles and the finite vortex nucleation time, using nonequilibrium quasiclassical (Keldysh-Usadel or Eilenberger) dynamics valid at $T << T_{c}$; time-dependent Ginzburg-Landau theory may be used only as a check near $T_{c}$. An answer gives $H_{\\mathrm{sh}}(f,T)/H_{\\mathrm{sh}}(0,T)$ for Nb and $\\mathrm{Nb_3Sn}$ and the frequency at which it departs from the static value.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.active-matter.active-nematic-order",
      "fields": {
        "title": {
          "text": "Do two-dimensional dry active nematics keep quasi-long-range order?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.active-matter.active-turbulence",
      "fields": {
        "title": {
          "text": "Is active turbulence described by universal statistical laws?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.amorphous-plasticity.brittle-ductile-yielding",
      "fields": {
        "title": {
          "text": "Is the brittle-to-ductile change in glass yielding a critical point?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Under athermal quasistatic shear, poorly annealed glasses yield smoothly (ductile) and well-annealed glasses yield through a macroscopic stress drop (brittle). A 2018 scenario maps this onto a random-field-Ising-like critical point at a preparation temperature $T_p,c$. Determine whether this critical point exists in the thermodynamic limit in $d = 2\\ \\text{and}\\ 3$, and its universality class, or whether brittle failure occurs for every preparation once the system is large enough.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.amorphous-plasticity.crack-microbranching",
      "fields": {
        "title": {
          "text": "What triggers microbranching of fast cracks in brittle amorphous solids?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.amorphous-plasticity.silica-nanoductility",
      "fields": {
        "title": {
          "text": "Is fracture of oxide glasses ductile at the nanometer scale?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For slow stress-corrosion cracks in silica and aluminosilicate glasses, determine whether crack advance involves a plastic process zone with nanocavities of size about $10^{-6}$ cm ahead of the tip, or atom-by-atom bond rupture with a process zone of a few bond lengths. An answer gives the process-zone size and the fraction of fracture energy dissipated plastically, from in situ imaging or matched fracture-surface analysis and simulations with reliable silica potentials.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.biological-clocks.segmentation-clock-tempo",
      "fields": {
        "title": {
          "text": "What sets the species-specific period of the segmentation clock?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.ecosystem-statphys.lv-phase-diagram",
      "fields": {
        "precise": {
          "text": "Consider $dN_{i}/dt=N_{i}(1-N_{i}-\\sum_{j}\\alpha_{ij}N_{j})+\\lambda$, $i=1..S$, with $\\alpha_{ij}$ of mean $\\mu/S$, standard deviation $\\sigma/\\sqrt{S}$, correlation $\\gamma$ between $\\alpha_{ij}$ and $\\alpha_{ji}$, and immigration $\\lambda$. Dynamical mean-field theory gives a unique globally attracting fixed point for $\\sigma<\\sigma_{c}=\\sqrt{2}/(1+\\gamma)$ as $S\\to\\infty$. Classify the phases for $\\sigma>\\sigma_{c}$ as functions of $\\gamma$ in $[-1,1]$ and $\\mu$, with $\\lambda\\to 0$: number and stability of fixed points, presence of chaos or aging, and whether the transitions are sharp. An answer is a phase diagram with order parameters, derived or established numerically at large $S$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.electrolytes-confined.confined-water-dielectric",
      "fields": {
        "precise": {
          "text": "For water in slits of height h between atomically flat graphite or hBN walls, the perpendicular dielectric constant falls to $\\epsilon_{\\mathrm{perp}} \\sim 2$ for $h \\sim 1\\ \\mathrm{nm}$ (2018 measurement), while a 2025 measurement found the in-plane constant $\\epsilon_{\\mathrm{par}}$ of about 1000 at few-layer thickness with superionic-level conductivity. Determine whether a model of interfacial layers with an anisotropic local dielectric tensor reproduces both $\\epsilon_{\\mathrm{perp}}(h)$ and $\\epsilon_{\\mathrm{par}}(h)$, or whether nonlocal correlated polarization and proton transport are required. An answer is a first-principles or simulation prediction of $\\epsilon_{\\mathrm{perp}}(h)$, $\\epsilon_{\\mathrm{par}}(h)$ and conductivity that matches both data sets.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.friction-wear.archard-wear-law",
      "fields": {
        "precise": {
          "text": "Archard's law $V = K N s / H$ (wear volume V, load N, sliding distance s, hardness H) has an empirical dimensionless coefficient K spanning roughly $10^{-8} \\text{ to } 10^{-2}$. Derive K from asperity-scale mechanisms, including the critical junction size $d*$ proportional to $G w / \\tau_j^{2}$ (shear modulus G, surface energy w, junction strength $\\tau_j$) below which junctions deform plastically instead of shedding debris, and predict wear rates for specified material pairs.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.friction-wear.superlubricity-scale",
      "fields": {
        "precise": {
          "text": "For a single continuous incommensurate crystalline contact (graphite on graphite or on hexagonal boron nitride; not an ensemble of many small superlubric flakes), the friction force scales as $F \\sim A^\\gamma$ with contact area $A$ and $\\gamma < 1$ because of edges, defects and elastic deformation. Determine $\\gamma$ and the crossover length above which elastic pinning or defects restore a finite friction per unit area, and whether friction coefficients below $10^{-3}$ can persist for two-dimensional contacts with area above about $10^{-4}\\,\\mathrm{cm}^2$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "Centimeter-long double-walled carbon nanotubes slide superlubrically (2013, a one-dimensional contact of small area), millimeter-scale superlubricity was reported in strained bilayer graphene (Androulidakis et al., Nat. Commun. 2020), and macroscale low friction has been obtained with many superlubric nanoflakes (2021-2024); a direct friction measurement on a single two-dimensional contact above about $10^{-4}\\ \\mathrm{cm}^{2}$ and the elastic-pinning crossover length are not established (2026).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.fragility-origin",
      "fields": {
        "title": {
          "text": "What sets the fragility of a glass-forming liquid?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "The kinetic fragility $m = d log10(\\tau_{\\alpha}) / d(T_{g}/T)$ evaluated at $T = T_g$ ranges from about 20 for $\\mathrm{SiO_2}$ to above 150 for some polymers. Identify the microscopic determinants of $m$ (softness of the repulsion, network connectivity, vibrational anharmonicity, the heat-capacity jump $\\Delta C_p$ at $T_g$) and give a predictive relation for $m$ tested across a set of chemically different liquids.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.growing-static-length",
      "fields": {
        "title": {
          "text": "Does a growing static length control relaxation near $T_g$?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.johari-goldstein-relaxation",
      "fields": {
        "precise": {
          "text": "In molecular glass formers, including glasses of rigid molecules, dielectric and mechanical spectra show a secondary $\\beta$ relaxation that persists below $T_g$ with Arrhenius $\\tau_\\beta(T)$ and an empirical activation energy of roughly $24\\ k_B T_g$ per molecule (approximate). Determine whether it is carried by localized islands of mobility or by small-angle motion of all molecules, and whether it is the precursor of the $\\alpha$ relaxation as assumed in coupling-type models. An answer identifies the motions in a model glass equilibrated near or below $T_{g}$ and reproduces the measured $\\beta$ peak and its link to $\\tau_\\alpha$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.kauzmann-ideal-glass",
      "fields": {
        "title": {
          "text": "Does an ideal glass transition occur at finite temperature in 3D?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.origin-of-slowdown",
      "fields": {
        "title": {
          "text": "What causes the super-Arrhenius slowdown of supercooled liquids?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In molecular glass formers the structural relaxation time $\\tau_\\alpha(T)$ grows from about $10^{-12}\\ \\mathrm{s}$ in the high-temperature liquid to about $10^{2}\\ \\mathrm{s}$ at $T_g$, with an effective activation energy that increases on cooling; model liquids (Kob-Andersen Lennard-Jones mixture, polydisperse soft spheres) reproduce the onset of this growth. Competing explanations include random first-order transition theory (entropy-driven cooperative rearrangements), dynamic facilitation (kinetically constrained localized excitations) and elastic or frustration-based models. An answer is a theory that predicts $\\tau_\\alpha(T)$ and the associated growing length scales from the interaction potential and is singled out against the alternatives by equilibrium simulations near and below the experimental $T_g$. This is the root question of the topic; its working content is split into the sharper problems linked to it.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.glass-transition.ultrastable-glass-limit",
      "fields": {
        "title": {
          "text": "How close can vapor-deposited glasses approach the ideal glass?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.granular-rheology.silo-clogging",
      "fields": {
        "title": {
          "text": "Is there a critical outlet size for clogging of granular silos?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For grains of diameter $d$ discharging through an orifice of diameter $D$, the mean number of grains $\\langle s\\rangle$ discharged between clogs grows with $D/d$. Determine whether $\\langle s\\rangle$ diverges at a finite critical $D_c/d$ as $(D_{c} - D)^{-\\gamma}$, or grows exponentially in a power of $D/d$ with no true transition, in 2D and 3D silos.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.jamming-rigidity.edwards-ensemble",
      "fields": {
        "title": {
          "text": "Does an Edwards-type ensemble describe granular packings away from jamming?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.jamming-rigidity.gardner-finite-d",
      "fields": {
        "title": {
          "text": "Does a true Gardner transition exist in three-dimensional glasses?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.jamming-rigidity.random-close-packing",
      "fields": {
        "title": {
          "text": "Is random close packing a well-defined density?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.jamming-rigidity.upper-critical-dimension",
      "fields": {
        "title": {
          "text": "Are jamming exponents mean-field already in two and three dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.lc-defects.ferroelectric-nematic-origin",
      "fields": {
        "precise": {
          "text": "Materials such as RM734 and DIO form a ferroelectric nematic phase $N_F$ with spontaneous polarization of about $2 \\times 10^{4}\\,\\mathrm{statC}/\\mathrm{cm}^{2}$; in DIO it is preceded by an antiferroelectric modulated phase ($\\mathrm{SmZ}_A$). Determine the molecular interactions (large longitudinal dipole of order $10^{-17}\\,\\mathrm{statC}\\,\\mathrm{cm}$, charge distribution along the molecule, steric shape) responsible for polar order, and give a criterion that predicts which molecular structures produce $N_F$ and the intermediate phase.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.lc-defects.thermotropic-biaxial-nematic",
      "fields": {
        "title": {
          "text": "Does a thermotropic biaxial nematic phase exist?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.lc-defects.twist-bend-mechanism",
      "fields": {
        "title": {
          "text": "What stabilizes the twist-bend nematic phase?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "The twist-bend nematic $N_{\\mathrm{TB}}$ (heliconical director, pitch about $8 \\times 10^{-7}\\ \\text{to}\\ 10^{-6}\\,\\mathrm{cm}$ in CB7CB) was predicted from a negative bend elastic constant $K_{33} < 0$ and alternatively explained through coupling to local polar order or flexoelectricity. Determine which mechanism stabilizes $N_{\\mathrm{TB}}$ and derive its coarse-grained elasticity (whether it behaves as a pseudo-layered smectic) from measured elastic constants and structure.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.morphogenesis-mechanics.shape-index-fluidity",
      "fields": {
        "precise": {
          "text": "The 2D vertex model with energy $E = \\sum_i [K_A (A_i - A_0)^2 + K_P (P_i - P_0)^2]$ ($A_i, P_i$ = cell area and perimeter) has a rigidity transition at target shape index $p_0 = P_0/\\sqrt{A_0} \\sim 3.81$. Determine whether the observed shape index $q = \\langle P/\\sqrt{A}\\rangle$ classifies fluid versus solid epithelia in vivo across tissues and species, or whether fluctuations, division and active tension remodeling set fluidity independently of q.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.nucleation.ice-homogeneous-rate",
      "fields": {
        "precise": {
          "text": "Determine the homogeneous ice nucleation rate $J(T)$ in pure $\\mathrm{H_2O}$ between about 230 and 240 K, where measurements by different techniques disagree by several orders of magnitude and simulations (seeding with TIP4P/Ice and similar models) depend on CNT-based extrapolation. Decide whether CNT with a temperature-dependent ice-water interfacial free energy $\\gamma(T)$ reproduces $J(T)$, and confirm whether the critical nucleus is stacking-disordered ice.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.nucleation.prenucleation-clusters",
      "fields": {
        "title": {
          "text": "Do stable prenucleation clusters exist in calcium carbonate solutions?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Clusters of about $20\\ \\mathrm{Angstrom}$ were reported in 2008 in undersaturated and supersaturated $\\mathrm{CaCO_3}$ solutions, with properties inconsistent with CNT. Determine whether they are thermodynamically stable solute species (negative formation free energy over a range of concentrations) or kinetically persistent ion associates or droplets of a dense liquid formed by liquid-liquid separation, from measured cluster size distributions and formation free energies versus concentration and pH.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.nucleation.tolman-length",
      "fields": {
        "precise": {
          "text": "For a nucleus of radius $R$, $\\gamma(R) = \\gamma_{\\infty}(1 - 2$ $\\delta$ $/ R + ...)$ with Tolman length $\\delta$. Determine the sign and magnitude of delta for the Lennard-Jones liquid-vapor interface and for crystal-melt interfaces, and whether the expansion in $1/R$ is valid at critical-nucleus sizes of about 10 to 30 Angstrom.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.nucleation.two-step-pathway",
      "fields": {
        "title": {
          "text": "When does crystal nucleation proceed in two steps?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.origin-of-life.error-threshold-paradox",
      "fields": {
        "precise": {
          "text": "With nonenzymatic copying fidelity $q \\sim 0.9\\ \\text{to}\\ 0.99$ per nucleotide, $L_{\\max} \\sim \\ln(\\sigma)/(1 - q)$ is tens to about a hundred nucleotides; polymerase ribozymes derived from the class I ligase are about 200 nucleotides long, while the 45-nucleotide QT45 ribozyme (Science 2026) copies at $q = 0.941$, giving $L_{\\max} \\sim 17 \\ln(\\sigma)$. Find a mechanism (compartments with group selection, hypercycles, template-directed ligation of short oligomers, spatial structure on surfaces) that maintains information content exceeding $L_{\\max}$ over many replication rounds, stable against parasitic sequences, for a replicase that copies itself from mononucleotides or mixed-length feedstocks, with parameters measured in prebiotic chemistry.",
          "how": [
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "A quantitative model with experimentally measured copying, ligation and compartment-division rates showing maintained information above $L_{\\max}$, ideally confirmed in an experiment.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.origin-of-life.rna-self-replicase",
      "fields": {
        "precise": {
          "text": "A polymerase ribozyme of length $L$ must synthesize complete copies of itself and of its complementary strand with per-nucleotide fidelity $q$ satisfying $L(1 - q) < \\ln(\\sigma)$ (Eigen error threshold; $\\sigma$ = selective advantage of the correct sequence), at yields that allow exponential growth over repeated cycles that include strand separation. QT45, a 45-nucleotide ribozyme (Gianni and co-workers, Science 2026), synthesizes its complementary strand from a random triplet pool at $q = 0.941$ and a copy of itself from defined triplet substrates, each at about 0.2% yield in 72 days in eutectic ice. Answer: yes or no, with a demonstrated system showing sustained exponential amplification of both strands over many rounds without defined oligomer feeds.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.polymer-dynamics.extensional-melt-solution",
      "fields": {
        "settled_by": {
          "text": "A constitutive model with independently measured parameters that reproduces $\\eta_{E}(eps_{dot})$ for melts and solutions, supported by rheo-optical or simulation measurements of the friction coefficient under flow.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.polymer-dynamics.lamellar-thickness",
      "fields": {
        "title": {
          "text": "What selects lamellar thickness in polymer crystals?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Flexible polymers crystallizing from melt or solution form chain-folded lamellae of thickness l around $10^{-6}\\,\\mathrm{cm}$, with $\\ell \\sim 1 / (T_m^{0} - T_c)$, where $T_m^{0}$ is the equilibrium melting temperature and $T_c$ the crystallization temperature. Lauritzen-Hoffman secondary nucleation, Sadler-Gilmer rough-surface growth and Strobl's mesomorphic-intermediate model give different mechanisms. Determine which mechanism selects l and the growth rate $G(T_c)$, by direct observation of the growth front in simulations of realistic chains or in situ scattering and microscopy.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.polymer-dynamics.shear-banding-entangled",
      "fields": {
        "title": {
          "text": "Do well-entangled polymer fluids form steady shear bands?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.polymer-dynamics.thin-film-tg",
      "fields": {
        "precise": {
          "text": "Free-standing polystyrene films thinner than about $8 \\times 10^{-6}$ cm (800 Angstrom) show $T_g$ reductions of tens of kelvin relative to bulk, with a dependence on molecular weight not seen in supported films. Determine whether the reduction arises from a mobile surface layer propagating into the film, from chain confinement or from another mechanism, and predict $T_g(h, M)$ for film thickness h and molecular weight $M$.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.polymer-dynamics.viscosity-exponent",
      "fields": {
        "title": {
          "text": "Does melt viscosity cross over to pure reptation scaling?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For monodisperse linear polymer melts, $\\eta_{0} \\sim$ $M^{3}$.4 is observed while pure reptation gives $M^{3}$; contour-length fluctuations and constraint release account for the difference at moderate $M / M_e$. Determine whether $\\eta_0$ crosses over to $M^3$ at very high $M / M_e$, and at what $M / M_e$, in experiment and in simulation.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Measurements of $\\eta_{0}$ for narrowly distributed melts extending to $M / M_{e}$ of order $10^{3}$ or more, or equivalent simulations, showing the local exponent approaching 3 or not.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.protein-folding.amyloid-nucleation",
      "fields": {
        "precise": {
          "text": "For A-beta42 at neutral pH and $\\alpha$-synuclein at mildly acidic pH (about 5 to 6) in vitro, aggregation kinetics fit a master equation in which secondary nucleation on fibril surfaces, at rate $k_{2}$ m^$n_{2}$ M (m = monomer concentration, M = fibril mass concentration), dominates the formation of new aggregates. Determine the microscopic steps (adsorption, conformational conversion on the surface, detachment) and compute $k_{2}$ and the reaction order $n_{2}$ from a molecular model, matching measured values within a factor of 3.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.protein-folding.sequence-to-rate",
      "fields": {
        "settled_by": {
          "text": "A blind test on newly measured folding rates of proteins absent from any training data, scored by root-mean-square error in $\\ln k_f$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.protein-folding.speed-limit",
      "fields": {
        "title": {
          "text": "What sets the folding speed limit and internal friction?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.quantum-biology.dna-proton-tunneling",
      "fields": {
        "precise": {
          "text": "For double proton transfer in Watson-Crick $G-C$ (and $A-T$) pairs producing tautomers such as $G*-C*$, compute the tautomer population in an open-quantum-system model at 310 K including tunneling and the bath, and the probability that a tautomer survives strand separation at the replication fork and is mispaired by the polymerase. Compare with spontaneous base-substitution rates of order $10^{-10}\\text{ to }10^{-9}$ per base per replication (approximately). An answer is the fraction of transition mutations attributable to proton-transfer tautomers, and the part of it due to tunneling as opposed to over-barrier transfer.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "A 2022 Communications Physics open-quantum-systems study found G-C tautomer occupation of about $1.7 \\times 10^{-4}$, with tunnelling exceeding over-barrier hopping by orders of magnitude, and a 2022 Communications Chemistry study found strand separation in the helicase can trap tautomers; polymerase misincorporation and comparison with measured mutation spectra remain untested.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.quantum-biology.rf-compass-disruption",
      "fields": {
        "precise": {
          "text": "Night-migratory songbirds reportedly lose magnetic orientation under broadband radio-frequency noise (reported from about $2\\,\\mathrm{kHz}$ up to about $85\\,\\mathrm{MHz}$, absent at $140\\text{-}150\\,\\mathrm{MHz}$) with magnetic amplitudes in the nanotesla range, about $10^{-5}\\text{ to }10^{-4}\\,\\mathrm{G}$. For a radical pair, a yield change of order 1 percent from a resonant field $B_{\\mathrm{rf}}$ requires $\\left(\\gamma_e B_{\\mathrm{rf}} T_2\\right)^2 \\sim 0.01$ with $\\gamma_e = 1.76 \\times 10^{7}\\,\\mathrm{s}^{-1}\\,\\mathrm{G}^{-1}$, giving $T_2$ of tens of microseconds or more at $B_{\\mathrm{rf}} \\sim 10^{-4}\\,\\mathrm{G}$ (heuristic estimate), far above computed relaxation times. An answer is a mechanism that reproduces the amplitude and frequency thresholds of the effect, within or outside the radical-pair picture, or a demonstration that the effect is not reproducible.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.supercooled-water.ambient-response-maxima",
      "fields": {
        "title": {
          "text": "Are water's compressibility maxima at 1 bar a Widom line?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "X-ray scattering on evaporatively cooled micro-droplets (2017) reported maxima of the isothermal compressibility $\\kappa_{T}$ and correlation length near 229 K at 1 bar. Determine whether these maxima lie on a Widom line (locus of response-function maxima emanating from an LLCP) by measuring $\\kappa_{T}(T)$ and the correlation length along several isobars up to about $10^{9}\\ \\mathrm{dyn}/\\mathrm{cm}^2$ and testing the growth of the maxima toward a critical point.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.supercooled-water.llcp-existence",
      "fields": {
        "title": {
          "text": "Does real water have a liquid-liquid critical point?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Determine whether $\\mathrm{H_2O}$ (and $\\mathrm{D_2O}$) has a first-order transition between a high-density liquid (HDL) and a low-density liquid (LDL) ending at a liquid-liquid critical point (LLCP), versus the singularity-free scenario, a critical point at negative pressure, or the stability-limit conjecture. The LLCP is established in several classical and machine-learned first-principles water models, and ultrafast heating of amorphous ice with X-ray scattering has reported a discontinuous-to-continuous crossover with critical fluctuations. An answer is an independent confirmation, by a different technique or group, of critical scaling (diverging correlation length with 3D Ising exponents) in metastable bulk water with crystallization excluded.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.supercooled-water.llcp-location",
      "fields": {
        "precise": {
          "text": "Assuming the LLCP exists, determine $(T_{c}, P_{c})$ for $\\mathrm{H_2O}$. Published model results and extrapolations from experiment span roughly $T_{c} = 170 \\text{ to } 230\\,\\mathrm{K}$ and $P_{c}$ from about $0 \\text{ to } 2 \\times 10^{9}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$ ($0 \\text{ to } 2\\,\\mathrm{kbar}$), all approximate. An answer is a measured or reliably computed $(T_{c}, P_{c})$ with error bars, consistent with thermodynamic data at accessible conditions.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.supercooled-water.polyamorphism-criterion",
      "fields": {
        "title": {
          "text": "Which liquids have liquid-liquid transitions, and why?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "First-order liquid-liquid transitions are reported in phosphorus and sulfur at high pressure and temperature and are debated in Si, $\\mathrm{SiO_2}$, triphenyl phosphite and some metallic glass formers. Find a criterion based on interaction potential and local structure (tetrahedral order, two competing local structures, softness of the repulsion) that predicts which single-component liquids show a liquid-liquid transition in the stable or metastable range, and test it across these systems.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "bio.supercooled-water.water-glass-transition",
      "fields": {
        "title": {
          "text": "Is the 136 K calorimetric step the glass transition of water?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.aqueous-interfaces.hofmeister-mechanism",
      "fields": {
        "precise": {
          "text": "Explain the anion ordering of the Hofmeister series (roughly SO4^2- > F- > Cl- > Br- > $\\mathrm{NO_3}$- > I- > $\\mathrm{ClO_4}$- > SCN-) in protein salting-out, nonpolar solute solubility and electrolyte surface tension, choosing among bulk water structure making and breaking, direct ion-solute pairing, interfacial adsorption driven by polarizability and partial dehydration, and ion-specific dispersion forces. An answer is a quantitative model with parameters from first principles or independent data that reproduces the ordering and its reversal on positively charged or hydrophobic surfaces.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.aqueous-interfaces.interfacial-field",
      "fields": {
        "precise": {
          "text": "Determine the mean electric field projected on a probe bond at the water-air and water-oil interfaces at 300 K, from vibrational Stark shifts of interface-specific probes and from ab initio molecular dynamics, and compare with bulk water. The answer is the field magnitude (reported values range up to about $3 \\times 10^{4}\\,\\mathrm{statvolt}/\\mathrm{cm}$) with its spatial profile across the interface.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.aqueous-interfaces.microdroplet-peroxide",
      "fields": {
        "precise": {
          "text": "For water microdroplets of radius 1 to 20 micrometers produced by spraying or condensation in an oxygen-free and ozone-free atmosphere, determine whether $\\mathrm{H_2O_2}$ forms at concentrations above 1 micromolar from water oxidation at the interface. An answer is a yes or no from controlled experiments that exclude dissolved oxygen, ozone, electrode and solid-contact sources, together with the energy source if yes.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "Isotope-labeled ($\\mathrm{H_2}$ 18O) experiments in rigorously controlled atmospheres with independent quantification of peroxide.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.aqueous-interfaces.salt-activity-prediction",
      "fields": {
        "precise": {
          "text": "For NaCl in water at 298 K and ambient pressure, compute from a molecular model not fitted to these data the solubility (measured about 6.15 mol/kg) and the mean ionic activity coefficient $\\gamma_{+-}(m)$ from 0.1 mol/kg to saturation within 5 percent, including the chemical potential of the crystal. An answer is a model and free-energy method meeting these targets that transfers to LiCl, KCl and $\\mathrm{CaCl_2}$ without refitting.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.aqueous-interfaces.surface-charge-sign",
      "fields": {
        "title": {
          "text": "Is the neat water surface acidic or basic?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For the interface of neat water (no surfactant impurities, pH 7, 300 K) with air or a hydrophobic liquid, determine the surface excess of H3O+ and OH- and the origin of the measured negative zeta potential (about -$2 \\times 10^{-4}$ statvolt at neutral pH for bubbles and oil drops), choosing between OH- adsorption, interfacial charge transfer between water molecules, and impurity effects. An answer is a quantitative account in which spectroscopic, electrokinetic and simulation results agree.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.catalytic-mechanisms.ab-initio-turnover",
      "fields": {
        "precise": {
          "text": "For benchmark heterogeneous reactions ($\\mathrm{NH_3}$ synthesis on Ru(0001) step sites, CO oxidation on Pt(111), methanol synthesis on Cu/ZnO), predict the absolute turnover frequency under specified temperature and pressure within a factor of 10 from first-principles energetics and kinetic modeling with no fitted parameters. An answer is a protocol (electronic structure accuracy, treatment of coverage, entropy and site heterogeneity) meeting this target on several reactions.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "A 2005 first-principles microkinetic model of $\\mathrm{NH_3}$ synthesis on Ru nanoparticles (Honkala et al., Science, https://doi.org/10.1126/science.1106435) matched measured rates to within about an order of magnitude, possibly helped by error cancellation; agreement across several reactions with controlled electronic-structure error is not established.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.catalytic-mechanisms.methanol-active-site",
      "fields": {
        "precise": {
          "text": "For Cu/ZnO/$\\mathrm{Al_2O_3}$ under industrial conditions (about 500 K, $5 \\times 10^{7}\\ \\text{to}\\ 10^{8}\\ \\mathrm{dyn}/\\mathrm{cm}^{2}$ of CO/$\\mathrm{CO_2}$/$\\mathrm{H_2}$), identify the site responsible for most methanol turnover: Zn-decorated Cu steps (Behrens et al., Science 2012, https://doi.org/10.1126/science.1219831), a Cu-Zn surface alloy whose Zn coverage sets the rate (Kuld et al., Science 2016, https://doi.org/10.1126/science.aaf0718), or the Cu-$\\mathrm{ZnO}_{x}$ interface, and whether the site differs for $\\mathrm{CO_2}$ and CO hydrogenation. An answer is operando identification of site structure correlated with site-normalized rates and reproduced by first-principles kinetics.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.catalytic-mechanisms.nitrogenase-n2-binding",
      "fields": {
        "precise": {
          "text": "For the E4 (Janus) state of FeMoco, determine the positions of the four added hydrogens (bridging hydrides, protonated sulfides), the site of $\\mathrm{N_2}$ binding (Fe2/Fe6 face, Mo, or after sulfide displacement), and the energetics of reductive elimination of $\\mathrm{H_2}$ coupled to $\\mathrm{N_2}$ binding. An answer is a structure and mechanism consistent with ENDOR/EPR data and with converged electronic-structure energetics.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.catalytic-mechanisms.oec-oxygen-bond",
      "fields": {
        "plain": {
          "text": "Plants split water using a cluster of four manganese atoms and one calcium atom. The step where two oxygen atoms join to make $\\mathrm{O_2}$ has not been directly seen.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For the $\\mathrm{Mn_4CaO_5}$ oxygen-evolving complex of photosystem II, identify the O-O bond-forming step in the S3 to S4 to S0 transition: which oxygen atoms couple (O5 with the inserted O6, or a water-derived ligand), the mechanism (oxyl-oxo radical coupling or nucleophilic attack), the Mn oxidation and spin states at the transition state, and its barrier consistent with the measured millisecond kinetics. An answer is a mechanism supported by time-resolved structural and spectroscopic data and by converged electronic-structure calculations.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.ciss.adsorption-effect-existence",
      "fields": {
        "title": {
          "text": "Do enantiomers adsorb differently on oppositely magnetized surfaces?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.dft-functionals.flat-plane-functional",
      "fields": {
        "precise": {
          "text": "Construct an exchange-correlation approximation, at cost no higher than a global hybrid, whose energy $E(N, S_z)$ is piecewise linear in fractional electron number N (no delocalization error) and constant in fractional spin at fixed N (no static correlation error), as tested on H2+ and $\\mathrm{H_2}$ dissociation, fractional-charge atoms and the stretched-bond benchmark sets, while keeping main-group thermochemistry errors below 3 kcal/mol. An answer is such a functional, or a proof that no functional of a given class can satisfy both conditions.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.electrode-interfaces.cation-effect-co2",
      "fields": {
        "title": {
          "text": "Origin of alkali cation effects in electrochemical $\\mathrm{CO_2}$ reduction",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "On copper and gold electrodes, $\\mathrm{CO_2}$ reduction barely works without metal cations in the solution, and larger cations such as cesium work better than lithium. Why the cation matters so much is unsettled.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{CO_2}$ reduction on Cu and Au electrodes in aqueous MHCO3 ($M = \\mathrm{Li}, \\mathrm{Na}, \\mathrm{K}, \\mathrm{Cs}$), identify the mechanism by which the cation controls the rate of the first $\\mathrm{CO_2}$ activation step and the product selectivity: interfacial field stabilization of adsorbed $\\mathrm{CO2}-$, direct coordination, local buffering of pH, or modification of the hydrogen-bond network. An answer is a model predicting partial current densities versus cation identity and concentration.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.electrode-interfaces.double-layer-structure",
      "fields": {
        "precise": {
          "text": "For Pt(111) and Au(111) in dilute aqueous perchlorate or fluoride electrolyte at 300 K, compute from first principles the potential of zero charge, the water orientation profile and the differential capacitance $C(\\phi)$ as a function of electrode potential $\\phi$, including the capacitance maximum near the potential of zero charge measured on Pt(111) and the Gouy-Chapman minimum at the potential of zero charge measured on Au(111) in dilute electrolyte. An answer is a simulation at fixed electrode potential that reproduces the measured potential of zero charge within $3.3 \\times 10^{-4}\\ \\mathrm{statvolt}$ and $C(\\phi)$ within 20 percent.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.electrode-interfaces.sei-formation",
      "fields": {
        "precise": {
          "text": "For graphite and lithium-metal anodes in carbonate electrolytes (for example 1 mol/L $\\mathrm{LiPF_6}$ in ethylene carbonate and ethyl methyl carbonate), determine the nanoscale arrangement of inorganic (LiF, $\\mathrm{Li_2CO_3}$, $\\mathrm{Li_2O}$) and organic phases in the solid-electrolyte interphase (SEI), the transport process that sustains its growth (electron tunneling, neutral lithium interstitial diffusion, solvent diffusion through pores), and the resulting thickness law $L(t)$, often reported near $t^{1/2}$. An answer is a model with first-principles rate parameters that predicts $L(t)$ and the measured calendar-aging capacity loss.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.liquid-water.anomalies-origin",
      "fields": {
        "settled_by": {
          "text": "Measurements of response functions inside the region of rapid crystallization (230 to 160 K) at pressures up to $3 \\times 10^{9}\\,\\mathrm{dyn}/\\mathrm{cm}^2$, compared with each scenario's predictions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.liquid-water.hydrated-electron-structure",
      "fields": {
        "title": {
          "text": "Does the hydrated electron occupy a cavity in liquid water?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.liquid-water.proton-transport-step",
      "fields": {
        "precise": {
          "text": "For an excess proton in liquid water at $300\\,\\mathrm{K}$, identify the rate-limiting step of structural (Grotthuss) diffusion, the relay of the proton from molecule to molecule: hydrogen-bond breaking or forming in the second solvation shell, or motion along the proton-transfer coordinate. An answer is a simulation with path-integral nuclei on a near-quantum-chemical potential that reproduces the measured proton diffusion coefficient (about $9.3 \\times 10^{-5}\\,\\mathrm{cm}^2/\\mathrm{s}$) and its H/D isotope effect and identifies the step from the trajectories.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.nonadiabatic-dynamics.organic-charge-transport",
      "fields": {
        "precise": {
          "text": "For high-mobility organic semiconductors (rubrene, pentacene, C8-BTBT) at 100 to 300 K, with transfer integrals of order 0.1 eV comparable to thermal fluctuations of these integrals, predict the mobility $\\mu(T)$ (measured about $3 \\times 10^{3}$ to $1.2 \\times 10^{4}$ $\\mathrm{cm}^2/(\\mathrm{statvolt}\\ \\mathrm{s})$ at room temperature in rubrene single crystals, lower in pentacene and C8-BTBT) and its temperature dependence from a microscopic model with ab initio parameters, deciding between transient localization, small-polaron and band pictures. An answer is a theory reproducing $\\mu(T)$ and the Hall and terahertz data.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.polaritonic-chemistry.vsc-rate-changes",
      "fields": {
        "title": {
          "text": "Do cavity-coupled vibrations change thermal reaction rates?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.reaction-dynamics.oh-methanol-low-t",
      "fields": {
        "precise": {
          "text": "For OH + $\\mathrm{CH_3OH}$ in Laval-nozzle flows from about 20 to 200 K, explain the rise of $k(T)$ by about two orders of magnitude below 200 K and its pressure dependence from a calculation combining the hydrogen-bonded pre-reaction complex, deep tunneling through the H-abstraction barrier and collisional stabilization, and determine $k(T)$ in the zero-pressure limit. An answer is a master-equation plus tunneling calculation on an accurate potential that reproduces measured $k(T, P)$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.reaction-dynamics.polyatomic-mode-selectivity",
      "fields": {
        "precise": {
          "text": "For abstraction reactions $X$ + $\\mathrm{CH_4}$ and $X$ + $\\mathrm{CHD_3}$ ($X = \\mathrm{H}, \\mathrm{F}, \\mathrm{Cl}, \\mathrm{O}$) and H + $\\mathrm{H_2O}$, predict the vibrational efficacy $\\eta_v$ (reactivity gain per unit energy in mode $v$ divided by that per unit translational energy) for each normal mode, and the bond selectivity, from properties of the potential near the transition state. An answer is a criterion tested against full-dimensional quantum scattering and crossed-beam data, including measured cases where C-H stretch excitation is no more effective than translation (Cl + $\\mathrm{CHD_3}$) or suppresses reaction (F + $\\mathrm{CHD_3}$ at low collision energy).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.reaction-dynamics.quantum-tst-deep-tunneling",
      "fields": {
        "precise": {
          "text": "Ring-polymer molecular dynamics transition-state theory (RPMD-TST) is the unique $t\\to 0+$ limit of a quantum flux-side time-correlation function and is exact when no recrossing of the dividing surface or its ring-polymer generalizations occurs (Hele and Althorpe, J. Chem. Phys. 2013, https://doi.org/10.1063/1.4792697). Below the crossover temperature $T_{x}=\\hbar\\omega_{b}/(2\\pi)$ ($\\omega_{b}=\\text{barrier frequency},\\ k_{B}=1$) it deviates from exact quantum rates for asymmetric barriers. Derive a rate theory without real-time dynamics whose error vanishes both without recrossing and in the semiclassical instanton limit, or rigorous bounds on the RPMD-TST error versus $T/T_{x}$ and barrier asymmetry, tested on Eckart barriers and H + $\\mathrm{H_2}$ type reactions.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.reaction-dynamics.water-isotope-effects",
      "fields": {
        "title": {
          "text": "Quantitative $\\mathrm{H_2O}$ versus $\\mathrm{D_2O}$ differences from first-principles quantum simulation",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Using path-integral simulations on a potential of coupled-cluster quality not fitted to isotope data, compute the $\\mathrm{H_2O}$ to $\\mathrm{D_2O}$ shifts of the temperature of maximum density (277.13 K versus about 284.3 K), the melting temperature (273.15 K versus about 276.97 K) and the viscosity ratio at 298 K (about 1.23), and decompose each into the competing quantum effects (hydrogen-bond weakening by intermolecular zero-point motion versus strengthening by O-H stretch delocalization). An answer is computed shifts within 1 K and 5 percent of experiment with the decomposition.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.reference-methods.cc-dmc-large-complexes",
      "fields": {
        "precise": {
          "text": "For noncovalent complexes of about 50 to 200 atoms (the coronene dimer, the $\\mathrm{C_{60}}$ in a cycloparaphenylene ring complex, and the L7 and S30L type sets), determine the basis-set-limit interaction energy $E_{\\int}$ to 0.5 kcal/mol and the source of the discrepancy of up to several kcal/mol between CCSD(T) and fixed-node diffusion Monte Carlo (DMC) reported in 2021. An answer is agreement between a modified coupled-cluster method and DMC with controlled fixed-node, time-step and finite-size errors on the same geometries.",
          "how": [
            "inside:operator-word",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "chem.strong-correlation.femoco-ground-state",
      "fields": {
        "precise": {
          "text": "For the resting state $E0$ of FeMoco ($\\mathrm{MoFe_7S_9C}$ cluster with homocitrate, total spin $S = 3/2$), determine the Fe oxidation-state distribution consistent with Mo(III), the spin-coupling pattern of the eight metal spins and the ordering of the lowest spin states, with energies converged to $1\\,\\mathrm{kcal}/\\mathrm{mol}$ in an active space large enough that the answer no longer changes with its size. An answer is a converged wavefunction calculation (or set of agreeing methods) that also reproduces measured Mossbauer, EPR and X-ray spectroscopic data.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "X-ray spectroscopy in 2014 (Bjornsson et al., Chem. Sci., https://doi.org/10.1039/c4sc00337c) identified a spin-coupled Mo(III), and a [$\\mathrm{MoFe_7S_9C}$]^1- charge state is favored; the Fe valence distribution, the spin-coupling pattern and converged spin-state energetics remain open.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.altermagnets.all-altermagnet-tmr",
      "fields": {
        "precise": {
          "text": "In an altermagnet/insulator/altermagnet junction (candidates CrSb, Cr-doped $\\mathrm{RuO_2}$, $\\mathrm{KV_2Se_2O}$, MnTe) with no ferromagnetic layer, measure $\\mathrm{TMR}=(R_{\\mathrm{AP}}-R_{\\mathrm{P}})/R_{\\mathrm{P}}$ at $T=300\\,\\mathrm{K}$, where P and AP denote parallel and antiparallel Neel vectors, and determine whether it exceeds 100 percent as nonrelativistic spin-splitting theory predicts. An answer is the measured TMR with device structure and evidence that it arises from the altermagnetic band splitting.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Work found for 2025-2026 is theoretical: a CrSb-based junction proposal (arXiv:2503.13850) and a first-principles all-altermagnet Cr-doped $\\mathrm{RuO_2}$/$\\mathrm{TiO_2}$/Cr-doped $\\mathrm{RuO_2}$ junction (arXiv:2607.21092); no experimental all-altermagnet junction with TMR above 100 percent at 300 K was found.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.altermagnets.ruo2-magnetic-state",
      "fields": {
        "title": {
          "text": "Is $\\mathrm{RuO_2}$ an altermagnet?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{RuO_2}$ was the first proposed metallic altermagnet, but muon and neutron measurements find no magnetic order in bulk crystals. Signals reported in thin films might come from surfaces or defects.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether stoichiometric rutile $\\mathrm{RuO_2}$ has collinear antiferromagnetic order with Ru moment above $10^{-3}\\,\\mu_B$, in bulk and in epitaxial films; if not, identify the origin of the anomalous Hall, spin-splitting torque and spin-resolved ARPES signals reported in films. An answer is a moment value or upper bound per sample type and a mechanism for the film signals.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Muon spin rotation and neutron diffraction (2024, arXiv:2405.10820) bound the bulk moment near $10^{-4}\\,\\mu_{\\mathrm{B}}$ per Ru; a 2026 preprint (arXiv:2604.10659) attributes film signals to surface ferrimagnetism.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.amorphous-low-temperature.thz-sound-damping",
      "fields": {
        "precise": {
          "text": "Below the boson-peak frequency $\\omega_{\\mathrm{BP}}$, scattering by elastic disorder predicts Rayleigh damping $\\Gamma \\sim \\omega^{d+1}$, while simulations of model glasses (Gelin, Tanaka and Lemaitre, Nature Materials 15, 1177, 2016) found $\\Gamma \\sim -\\omega^{d+1}\\ln(\\omega)$, attributed to long-range spatial correlations of the elastic constants. Determine the asymptotic form of $\\Gamma(\\omega)$ in $d = 3$ glasses, its dependence on glass stability, its crossover to the Ioffe-Regel limit near $\\omega_{\\mathrm{BP}}$, and its link to the plateau of thermal conductivity near 10 K.",
          "how": [
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "Inelastic x-ray or ultraviolet Brillouin scattering on one glass over a decade of frequency below $\\omega_{\\mathrm{BP}}$, with resolution sufficient to separate $\\omega^4$ from $\\omega^4 \\ln(\\omega)$, matched to simulations of the same glass at several stabilities.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.amorphous-low-temperature.tls-identity",
      "fields": {
        "precise": {
          "text": "For amorphous $\\mathrm{SiO_2}$ (and a-Si, a-Al2O3), identify the atomic configurations that form tunneling two-level systems with energies below $\\sim 10^{-4}\\,\\mathrm{eV}$ ($\\sim 1\\,\\mathrm{K}$), and reproduce their measured density of states $P$, deformation potential $\\gamma \\sim 0.5-1\\,\\mathrm{eV}$, electric dipole moments and isotope dependence.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.amorphous-low-temperature.ultrastable-depletion",
      "fields": {
        "precise": {
          "text": "Vapor-deposited ultrastable indomethacin (Perez-Castaneda et al. 2014) shows strongly reduced tunneling-defect density, e-beam deposited hydrogen-free a-Si films showed no detectable tunneling states (Liu et al., Physical Review Letters 113, 025503, 2014), and simulations of glasses prepared by swap Monte Carlo find the defect density falling steeply with decreasing fictive temperature $T_f$ (Khomenko et al. 2020). Determine $P(T_f)$ for network glasses such as $\\mathrm{SiO_2}$ and whether the a-Si result generalizes, i.e. whether $P \\to 0$ at finite $T_f$ or only in the ideal-glass limit.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.amorphous-low-temperature.universal-tunneling-strength",
      "fields": {
        "precise": {
          "text": "Below $\\sim 1\\,\\mathrm{K}$ amorphous solids show specific heat $C \\sim T$, thermal conductivity $\\kappa \\sim T^{2}$ and an internal-friction plateau $Q^{-1} = (\\pi/2) C_{\\mathrm{tun}}$, with tunneling strength $C_{\\mathrm{tun}} = P \\gamma^{2}/(\\rho v^{2})$ between $\\sim 10^{-4}$ and $10^{-3}$ across chemically different glasses ($P$ = density of states of tunneling two-level systems, $\\gamma$ = deformation potential, $\\rho$ = mass density, $v$ = sound velocity); equivalently the phonon mean free path is $\\sim 150$ wavelengths. Explain this universality, e.g. by interaction-induced renormalization of the defects (Yu and Leggett; Burin and Kagan) or by a generic soft-mode mechanism, and predict where it fails.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A theory deriving $C_{\\mathrm{tun}} \\sim 10^{-4} \\text{ to } 10^{-3}$ from generic properties of glasses, confirmed by a predicted exception or by simulations that compute $P$ and $\\gamma$ in several model glasses.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.chaos-scrambling.bound-saturation",
      "fields": {
        "title": {
          "text": "Can a lattice with few states per site saturate the chaos bound?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.chaos-scrambling.diffusion-butterfly-bound",
      "fields": {
        "title": {
          "text": "Is energy diffusion bounded above by the butterfly velocity?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.contact-electrification.carrier-identity",
      "fields": {
        "title": {
          "text": "Which species carry charge between contacting insulators?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.contact-electrification.charge-mosaic",
      "fields": {
        "precise": {
          "text": "Kelvin probe force microscopy after contact (Baytekin et al., Science 2011) shows mosaics of positive and negative patches of lateral size about $10^{-5}$ to $10^{-4}$ cm with local densities far above the net charge density. Determine the mechanism (transfer of material carrying radicals and ions, heterogeneous surface chemistry, local discharges, flexoelectric polarization from contact strain) and the patch-size statistics, and how the mosaic relates to the net charge. An answer is a mechanism with a predicted patch-size distribution.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.contact-electrification.humidity-history",
      "fields": {
        "precise": {
          "text": "Contact charge depends non-monotonically on relative humidity (often peaking at intermediate values) and evolves with repeated contacts and rubbing. Determine the roles of adsorbed water thickness (as ion source and as leakage path), surface ion mobility and mechanochemical surface change, and give a model predicting charge versus relative humidity and contact number for benchmark pairs (e.g. PTFE-glass, $\\mathrm{SiO_2}$-$\\mathrm{SiO_2}$). An answer is a model validated on controlled-atmosphere data.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.crystal-plasticity.avalanche-universality",
      "fields": {
        "precise": {
          "text": "Compression of micropillars (Dimiduk et al. 2006) and acoustic emission in ice and metals give slip-size distributions $P(S) \\sim S^{-\\tau} \\exp(-S/S_{0})$ with $\\tau \\sim 1.5 \\text{ to } 1.6$. Determine whether the critical behavior is mean-field depinning ($\\tau = 3/2, S_{0} \\sim (\\sigma_{c} - \\sigma)^{-2}$), a distinct class set by long-range dislocation interactions, or criticality without a tuning parameter, and how $\\tau$ depends on crystal structure (FCC versus BCC) and temperature. An answer is a classification with $\\tau$, cutoff scaling and average avalanche shape.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.crystal-plasticity.inverse-hall-petch",
      "fields": {
        "precise": {
          "text": "Hall-Petch strengthening $\\sigma_y = \\sigma_0 + k$ $d$^-1/2 ($d$ the grain size) fails below $d$ of roughly $10^{-6}$ to $2 \\times 10^{-6}$ cm in Cu, Ni and other metals. Determine the critical grain size $d_c$ and the softening mechanism below it (grain-boundary sliding, grain rotation, boundary-mediated dislocation emission, or processing artifacts such as porosity and impurities), and whether boundary relaxation or solute segregation can suppress softening altogether. An answer is $d_c$ and the mechanism from artifact-free samples, matched by simulation.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.crystal-plasticity.micropillar-size-effect",
      "fields": {
        "precise": {
          "text": "Flow stress of FCC micropillars scales as $\\tau \\sim D^{-n}$ with $n \\sim 0.6 \\text{ to } 0.7$ for diameters D from about $10^{-5} \\text{ to } 10^{-3}\\,\\mathrm{cm}$ (Uchic et al. 2004), while BCC metals show smaller n correlated with the temperature dependence of screw dislocation mobility. Determine which mechanism (truncation of single-arm sources, dislocation starvation, exhaustion hardening) controls n, and whether n is universal for FCC, via 3D dislocation dynamics compared with experimental statistics. An answer is the mechanism with predicted n versus material, D and initial dislocation density.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.crystal-plasticity.psb-crack-initiation",
      "fields": {
        "precise": {
          "text": "In cyclically loaded Cu single crystals, persistent slip bands with dislocation ladder walls spaced about $10^{-4}$ cm carry localized plastic strain and produce surface extrusions and intrusions where cracks nucleate. Determine the mechanism producing extrusions (vacancy generation by annihilation of edge dislocation dipoles, as in the Essmann-Gosele-Mughrabi model, or irreversible slip) and predict the number of cycles to crack initiation versus plastic strain amplitude. An answer is a model validated against measured extrusion growth rates and initiation lives.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.crystal-plasticity.tin-whiskers",
      "fields": {
        "precise": {
          "text": "Electroplated Sn films on Cu grow single-crystal whiskers of diameter about $10^{-4}$ to $10^{-3}$ cm and length up to about 1 cm. Determine the driving force (compressive stress from $\\mathrm{Cu_6Sn_5}$ intermetallic growth relieved by grain-boundary diffusion under a surface oxide, recrystallization of grains with oblique boundaries, or other contributions) and predict which grains grow whiskers, the incubation time and the growth rate versus stress and temperature. An answer is a model verified on films with controlled stress and microstructure.",
          "how": [
            "outside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprate-pseudogap.origin",
      "fields": {
        "title": {
          "text": "What is the pseudogap state of underdoped cuprates?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprate-pseudogap.oscillation-pockets",
      "fields": {
        "title": {
          "text": "What reconstructs the underdoped cuprate Fermi surface into small pockets?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprate-pseudogap.pstar-critical-point",
      "fields": {
        "title": {
          "text": "Is the pseudogap endpoint $p*$ a quantum critical point?",
          "how": [
            "ai:gpt-5.5",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "With superconductivity suppressed by fields of several hundred kG, determine whether the endpoint $p*$ (0.19 to 0.23 depending on family) is a quantum critical point with an order parameter ($C/T \\sim \\log(1/T)$, Hall number change from $p\\ \\text{to}\\ 1+p$) or a change of Fermi-surface topology without broken symmetry. An answer identifies the transition type and, if one exists, the order parameter whose fluctuations give the log divergence.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprate-pseudogap.tstar-transition",
      "fields": {
        "title": {
          "text": "Is the pseudogap temperature $T*$ a thermodynamic phase transition?",
          "how": [
            "ai:gpt-5.5",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In a clean hole-doped cuprate (YBa2Cu3O6+x or HgBa2CuO4+d), determine whether the free energy is nonanalytic along $T*(p)$: resolve a specific-heat or thermal-expansion anomaly at $T*$ matching the symmetry breaking claimed by polarized neutron scattering, torque magnetometry and polar Kerr rotation, or bound $\\Delta C/T$ below the value required by a mean-field transition with the claimed order parameter. An answer is a detected singularity with its exponent, or such a bound.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Resonant ultrasound (2013) found an elastic anomaly along $T*(p)$, and torque magnetometry (2017) and polarized neutron data indicate symmetry breaking near $T*$, but no calorimetric anomaly at $T*$ has been resolved and the neutron results are disputed.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprates.charge-transfer-tc",
      "fields": {
        "title": {
          "text": "Does the charge-transfer gap set the maximum $T_{c}$ across cuprate families?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For hole-doped cuprates at optimal doping, test whether $T_c,\\mathrm{max}$ and the zero-temperature pair density decrease monotonically with the charge-transfer energy $\\Delta_{\\mathrm{CT}}$ (equivalently increase with $J\\sim t_{\\mathrm{pd}}^4/\\Delta_{\\mathrm{CT}}^3$), as superexchange pairing in the three-band Emery model predicts. An answer is a cross-family data set ($\\Delta_{\\mathrm{CT}}$ from optics or tunneling, $T_c,\\mathrm{max}$, superfluid density) with a quantitative fit to model predictions, or a counterexample family.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprates.overdoped-superfluid",
      "fields": {
        "precise": {
          "text": "In overdoped La2-xSrxCuO4 films the zero-temperature phase stiffness $\\rho_s0$ is proportional to $T_c$ and far below the BCS value expected from the normal-state Drude weight (2016). Determine whether d-wave BCS theory with realistic (forward and point) disorder accounts quantitatively for $\\rho_s0(p)$, the T-linear $\\rho_s(T)$, and the residual uncondensed Drude weight seen in terahertz optics, or whether intrinsic inhomogeneity or a different pairing state is required.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprates.pairing-mechanism",
      "fields": {
        "title": {
          "text": "What interaction binds electrons into pairs in the cuprates?",
          "how": [
            "title:owner"
          ]
        },
        "precise": {
          "text": "Identify the dominant pairing interaction behind $d_{(x^{2}-y^{2})}$ superconductivity in hole-doped $\\mathrm{CuO_2}$ planes (candidates: antiferromagnetic superexchange $J \\sim 0.13\\ \\mathrm{eV}$ and spin fluctuations, charge-transfer fluctuations, phonons, or a combination). An answer is a microscopic mechanism that predicts $T_c(p)$ and the gap magnitude across cuprate families within a factor of order one and passes material-specific tests (isotope effect, pressure dependence, family dependence of $T_c,\\mathrm{max}$).",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprates.pdw-existence",
      "fields": {
        "title": {
          "text": "Is there a bulk pair density wave in any cuprate?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.cuprates.twisted-trsb",
      "fields": {
        "title": {
          "text": "Does 45-degree twisted $\\mathrm{Bi2Sr2CaCu2O8}+x$ break time-reversal symmetry?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.bismuth-pairing",
      "fields": {
        "precise": {
          "text": "High-purity Bi single crystals superconduct at $T_{c} \\sim 0.53\\,\\mathrm{mK}$ (Prakash et al., Science 2017) with carrier density about $3 \\times 10^{17}\\,\\mathrm{cm}^{-3}$, Fermi energies of order $25\\,\\mathrm{meV}$ comparable to the Debye energy of order $10\\,\\mathrm{meV}$, so the Migdal adiabatic approximation fails. Compute $T_{c}$ from a controlled theory (Dirac-like bands with phonon coupling and screening) and determine the pairing symmetry. An answer is a mechanism giving $T_{c}$ within a factor of about 2 together with the predicted gap symmetry.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.ferroelectric-critical-enhancement",
      "fields": {
        "title": {
          "text": "Does ferroelectric quantum criticality raise the $T_{c}$ of $\\mathrm{SrTiO_3}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "$\\mathrm{SrTiO_3}$ is close to becoming ferroelectric, meaning its ions almost shift to create a permanent electric dipole. Pushing it closer, by replacing oxygen-16 with oxygen-18 or adding calcium, raises its superconducting temperature, and the reason is debated.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "18O substitution, Ca substitution and strain move n-doped $\\mathrm{SrTiO_3}$ toward its ferroelectric quantum critical point and raise $T_c$, in some reports by about a factor of 2. Determine whether the enhancement is caused by pairing through the critical soft transverse-optical mode, which electron-phonon coupling is responsible (linear Rashba-type or bilinear two-phonon), and where $T_c$ peaks relative to the critical point (paraelectric side, at criticality, or inside the polar phase). An answer is a mechanism with a quantitative fit of $T_c$ versus distance to criticality and carrier density.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.fese-bcs-bec",
      "fields": {
        "title": {
          "text": "Is superconducting $\\mathrm{FeSe}1-x\\mathrm{S}x$ in the BCS-BEC crossover regime?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.laalo3-dome",
      "fields": {
        "title": {
          "text": "Origin of the superconducting dome at $\\mathrm{LaAlO_3}$/$\\mathrm{SrTiO_3}$ interfaces",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Where $\\mathrm{LaAlO_3}$ meets $\\mathrm{SrTiO_3}$, a thin conducting sheet forms that superconducts below about $0.3\\,\\mathrm{K}$, and a gate voltage tunes its transition temperature up and then down. What causes this dome-shaped curve is unresolved.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "The two-dimensional electron gas at (001) $\\mathrm{LaAlO_3}$/$\\mathrm{SrTiO_3}$, with sheet density $n_{s}$ of order $10^{13}\\,\\mathrm{cm}^{-2}$, shows a gate-tuned dome $T_{c}(V_{g})$ with maximum about $0.2\\ \\text{to}\\ 0.3\\,\\mathrm{K}$ near a Lifshitz transition where $d_{xz}/d_{yz}$ subbands fill and Rashba spin-orbit coupling grows. Determine the cause of the decrease of $T_{c}$ on both sides of the maximum (multiband pairing, loss of superfluid stiffness and phase fluctuations, change of dielectric screening) from a calculation matching $T_{c}(n_{s})$, superfluid stiffness and tunneling gap data. An answer is a quantitative model of the dome.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.srtio3-pairing",
      "fields": {
        "title": {
          "text": "What pairs electrons in doped $\\mathrm{SrTiO_3}$ at Fermi energies below phonons?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Electron-doped $\\mathrm{SrTiO_3}$ (Nb, La or oxygen vacancies) superconducts from $n\\ \\text{below}\\ 1\\mathrm{e}18\\,\\mathrm{cm}^{-3}\\ \\text{to about}\\ 1\\mathrm{e}21\\,\\mathrm{cm}^{-3}$ with maximal $T_c$ of approximately $0.4\\,\\mathrm{K}$ near $n \\sim 1\\mathrm{e}20\\,\\mathrm{cm}^{-3}$; at the lowest densities $E_F \\sim 1\\,\\mathrm{meV}$ is far below the longitudinal optical phonon energies (up to about $100\\,\\mathrm{meV}$). Identify the pairing interaction (soft transverse-optical mode via two-phonon or Rashba-type coupling, dynamically screened longitudinal-optical phonons and plasmons, or other) that reproduces $T_c(n)$ quantitatively over the full dome without adjustable couplings. An answer is a mechanism with computed $T_c(n)$ within a factor of about 2.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dilute-superconductivity.yptbi-j32-pairing",
      "fields": {
        "precise": {
          "text": "YPtBi ($\\Gamma_{8}$ band, $n \\sim 2 \\times 10^{18}\\ \\mathrm{cm}^{-3}$, $T_{c} \\sim 0.78\\ \\mathrm{K}$) shows a penetration depth linear in $T$ suggesting line nodes (Kim et al., Science Advances 2018) and an upper critical field above the Pauli limit. Identify the order parameter among $j = 3/2$ pairing channels (septet $J = 3$, quintet $J = 2$, singlet-septet mixture allowed by broken inversion) and its pairing interaction. An answer is a symmetry identification consistent with penetration depth, NMR, critical-field and tunneling data.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.disordered-frustrated-magnets.h3liir2o6-ground-state",
      "fields": {
        "title": {
          "text": "Is $\\mathrm{H_3LiIr_2O_6}$ a bond-disordered Kitaev spin liquid?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{H_3LiIr_2O_6}$ is a honeycomb iridium oxide that shows no magnetic order down to the lowest temperatures measured. The hydrogen atoms between its layers are disordered, and it is unclear whether its state is a Kitaev spin liquid altered by random couplings or a collection of random spin pairs unrelated to Kitaev physics.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{H_3LiIr_2O_6}$ (no magnetic order detected down to tens of mK, $C/T$ diverging at low $T$ with $H/T$ scaling), determine whether the low-energy density of states and the scaling of $C/T$ arise from random Majorana hopping and fluxes bound to vacancies in a Kitaev spin liquid (Knolle, Moessner, Perkins, PRL 2019), or from random singlets of local moments without Kitaev fractionalization. An answer identifies the ground state with measured and calculated low-energy density of states agreeing within errors.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.disordered-frustrated-magnets.random-singlet-scaling",
      "fields": {
        "precise": {
          "text": "In $\\mathrm{H_3LiIr_2O_6}$ and several other disordered frustrated magnets the data obey $C/T \\sim T^{-\\gamma} F_C(\\mu_B H/k_B T)$ and $M \\sim H^{(1-\\gamma)} F_M(\\mu_B H/k_B T)$ with a material-dependent $\\gamma$ between 0 and 1 (Kimchi, Sheckelton, McQueen, Lee, Nature Communications 2018), attributed to a power-law distribution of singlet energies $P(J) \\sim J^{-\\gamma}$. Derive $\\gamma$ and the scaling functions $F_C, F_M$ from a microscopic disordered model of at least one compound, and determine whether $\\gamma$ is fixed by a 2D random-singlet fixed point or is nonuniversal. An answer is a model whose computed $\\gamma$ and $F_C$ agree with the data without fitting $\\gamma$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.disordered-frustrated-magnets.ybmggao4-ground-state",
      "fields": {
        "title": {
          "text": "Is $\\mathrm{YbMgGaO_4}$ a spin liquid or a disorder-driven state?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{YbMgGaO_4}$ is a triangular-lattice magnet with no detected order and a broad continuum of spin excitations, first read as a spin-liquid signature. Its magnesium and gallium atoms are randomly mixed, which makes the couplings random, and that alone may produce the same data.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{YbMgGaO_4}$ (effective $S = 1/2$ Yb3+ doublets on a triangular lattice, nearest-neighbor exchange of order 0.1 meV, random Mg/Ga site mixing), determine whether the $T \\to 0$ ground state is a quantum spin liquid with fractionalized spinons, a random-singlet (valence-bond glass) state, or a spin glass. An answer names the state with evidence that discriminates the three: the field and temperature scaling of $C$ and $\\chi$, ac-susceptibility freezing below 0.1 K, and whether the neutron continuum is reproduced by a disordered model without fractionalization.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Zhu et al. (PRL 2017) reproduced the continuum by bond disorder acting on a model whose clean ground state is stripe ordered, Kimchi et al. (PRX 2018) proposed a random-singlet state, and Ma et al. (PRL 2018) found spin-glass freezing in the sister compound $\\mathrm{YbZnGaO_4}$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dqpt.equilibrium-criticality-link",
      "fields": {
        "title": {
          "text": "Do dynamical transitions occur only for quenches across critical points?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For a quench $H_i \\to H_f$ with Loschmidt rate $l(t) = -\\lim_{N \\to \\infty} (1/N) \\ln \\mid\\langle\\psi_0\\mid \\exp(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$, determine the conditions on $(H_i, H_f)$ under which nonanalytic times $t_c$ exist if and only if the quench crosses an equilibrium critical point. Known counterexamples from 2014 on violate both directions in specific models. Answer: a criterion valid for interacting nonintegrable models.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dqpt.local-observable-signature",
      "fields": {
        "title": {
          "text": "Can a local measurement detect a dynamical transition in large systems?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dqpt.mixed-state-generalization",
      "fields": {
        "title": {
          "text": "Do dynamical quantum phase transitions survive at finite temperature?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dqpt.order-parameter-connection",
      "fields": {
        "precise": {
          "text": "For a quench $H_i \\to H_f$, the Loschmidt rate $l(t) = -\\lim_{N \\to \\infty} (1/N) \\ln \\mid\\langle\\psi_0\\mid \\exp(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$ can be nonanalytic at critical times $t_c$. Determine conditions on $(H_i, H_f)$ under which (a) such $t_c$ exist if and only if the quench crosses an equilibrium critical point and (b) $t_c$ coincide with zeros or sign changes of the order parameter. Answer: a classification valid beyond free-fermion models.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.dqpt.order-parameter-zeros",
      "fields": {
        "title": {
          "text": "Do dynamical transition times coincide with zeros of the order parameter?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.driven-dissipative.dissipative-time-crystal",
      "fields": {
        "title": {
          "text": "Can short-range open quantum systems host stable continuous time crystals?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.driven-dissipative.kpz-2d-condensate",
      "fields": {
        "title": {
          "text": "Does KPZ physics destroy order in two-dimensional polariton condensates?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.electron-dephasing-mesoscopic.quantum-dot-saturation",
      "fields": {
        "precise": {
          "text": "In open GaAs/AlGaAs quantum dots, $\\tau_\\phi$ extracted from weak-localization and conductance-fluctuation statistics saturates at low $T$; Huibers et al. (Physical Review Letters 83, 5090, 1999) studied this saturation together with the dephasing caused by applied microwave radiation. Identify the limiting source (residual electron heating, external radiation, charge fluctuators in the heterostructure, nuclear spins) from the dependence of the saturated $\\tau_\\phi$ on dot size, lead coupling and independently measured electron temperature.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.electron-hydro.dyakonov-shur-instability",
      "fields": {
        "title": {
          "text": "Is the Dyakonov-Shur plasma-wave instability observable in a real device?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.electron-hydro.tomographic-regime",
      "fields": {
        "title": {
          "text": "Do two-dimensional Fermi liquids show odd-even tomographic relaxation?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.eth.golden-rule-scaling",
      "fields": {
        "title": {
          "text": "Does the relaxation rate scale as $g^{2}$ in the thermodynamic limit?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.excitonic-insulators.ta2nise5-gap-origin",
      "fields": {
        "title": {
          "text": "Is the gap of $\\mathrm{Ta_2NiSe_5}$ excitonic or lattice driven?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "$\\mathrm{Ta_2NiSe_5}$ becomes insulating below about 326 K, and at the same temperature its crystal distorts slightly. It is unclear whether electron-hole attraction or the lattice distortion opens the gap.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "$\\mathrm{Ta_2NiSe_5}$ has an orthorhombic-to-monoclinic transition at $T_c \\sim 326\\,\\mathrm{K}$ with valence-band flattening and a gap of order 0.1 eV seen in photoemission; the excitonic and structural order parameters have the same symmetry and so coexist. Determine which instability drives the transition, i.e. whether a purely electronic (excitonic) susceptibility diverges at $T_c$ with the lattice frozen, or whether the cooperative zone-center phonon distortion is primary, and what fraction of the low-temperature gap each produces. An answer is an identified primary order parameter with a quantitative partition of the gap.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.excitonic-insulators.tise2-cdw-origin",
      "fields": {
        "title": {
          "text": "Is the charge-density wave of 1T-TiSe2 an exciton condensate?",
          "how": [
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "$\\mathrm{TiSe_2}$ forms a charge-density wave (a periodic ripple of electron density and atom positions) below about 200 K. One experiment reported a softening electronic mode pointing to exciton condensation, while a 2025 calculation concluded that lattice fluctuations alone open the gap.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "A 2025 quasiparticle self-consistent many-body calculation (Pashov et al., npj Computational Materials) concluded that $\\mathrm{TiSe_2}$ is a band insulator produced by lattice fluctuations, against the 2017 soft-plasmon interpretation.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.excitonic-insulators.tmd-exciton-superfluid",
      "fields": {
        "title": {
          "text": "Is the $\\mathrm{MoSe_2}$/$\\mathrm{WSe_2}$ dipolar excitonic insulator an exciton superfluid?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{MoSe_2}$/hBN/$\\mathrm{WSe_2}$ electron-hole double layers at equal densities $n_e = n_h$ of order $10^{11} \\text{ to } 10^{12}\\,\\mathrm{cm}^{-2}$, 2025 Coulomb-drag experiments found a drag ratio near 1 (perfect drag), showing transport by bound excitons. Determine whether the exciton fluid has a finite superfluid stiffness below a Berezinskii-Kosterlitz-Thouless temperature $T_{\\mathrm{BKT}}$, i.e. vanishing counterflow resistance or a Josephson-like interlayer response, and give $T_{\\mathrm{BKT}}$ versus density. An answer is yes or no with measured $T_{\\mathrm{BKT}}(n)$.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.excitonic-insulators.wte2-excitonic",
      "fields": {
        "title": {
          "text": "Is the insulating state of monolayer $\\mathrm{WTe_2}$ an excitonic insulator?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Monolayer $\\mathrm{WTe_2}$ is insulating at charge neutrality and conducts along its edges. Experiments suggest the bulk gap comes from electron-hole pairing, but a gap from ordinary band mixing or disorder has not been ruled out.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ferroelectric-polar-textures.hfo2-ferroelectricity",
      "fields": {
        "title": {
          "text": "What stabilizes ferroelectricity and wake-up in thin-film $\\mathrm{HfO_2}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Doped (Si, Zr, La, Y) $\\mathrm{HfO_2}$ films of thickness about $5 \\times 10^{-7}$ to $2 \\times 10^{-6}$ cm show remanent polarization of order $3 \\times 10^{4} \\text{ to } 9 \\times 10^{4}\\,\\mathrm{statC}/\\mathrm{cm}^{2}$, attributed mainly to the metastable orthorhombic $\\mathrm{Pca2}_{1}$ phase. Determine which factors stabilize it (surface and grain-boundary energy, dopants, oxygen vacancies, stress, electrodes), whether other polar phases contribute, and the mechanism of wake-up and fatigue (oxygen-vacancy redistribution versus field-induced transformation from tetragonal or monoclinic grains). An answer is a phase-stability and switching model predicting remanent polarization versus thickness, dopant and cycle number.",
          "how": [
            "outside:e-notation",
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ferroelectric-polar-textures.polar-nanoregions",
      "fields": {
        "precise": {
          "text": "In Pb(Mg1/3Nb2/3)$\\mathrm{O_3}$ (PMN) and $\\mathrm{PMN}-x\\mathrm{PbTiO3}$, diffuse scattering and frequency-dispersive dielectric response (Vogel-Fulcher freezing near approximately 220 K in PMN) indicate polar correlations below a Burns temperature of approximately 600 K. Determine their structure (size distribution and correlation length versus $T$; discrete nanoregions versus a continuous slush of nanodomains) and their cause (random electric fields from B-site charge disorder, random bonds, or local strain) with a first-principles-based effective Hamiltonian validated against diffuse-scattering line shapes. An answer is a model reproducing the diffuse scattering and dielectric dispersion.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ferroelectric-polar-textures.sliding-switching",
      "fields": {
        "plain": {
          "text": "Stacking two layers of boron nitride or of a semiconductor like $\\mathrm{MoS_2}$ in a particular offset creates an electric dipole between them that flips when one layer slides by one atomic spacing. How the sliding proceeds through moving boundaries between domains, and what limits its speed and endurance, is unclear.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fese-sto-interface.enhancement-mechanism",
      "fields": {
        "title": {
          "text": "Why does $\\mathrm{SrTiO_3}$ raise the transition temperature of monolayer FeSe?",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Monolayer FeSe/$\\mathrm{SrTiO_3}$(001) has only electron pockets at M (about 0.1 e per Fe), with a gap of $\\sim 15-20\\,\\mathrm{meV}$ that closes near $55-65\\,\\mathrm{K}$ in photoemission, while electron-doped FeSe without $\\mathrm{SrTiO_3}$ (K dosing, ionic gating) reaches $\\sim 40-48\\,\\mathrm{K}$. Determine the separate contributions to $T_c$ of electron doping, interfacial electron-phonon coupling to $\\mathrm{SrTiO_3}$ polar (Fuchs-Kliewer) phonons at $\\sim 80-100\\,\\mathrm{meV}$ through small-momentum forward scattering, and substrate screening.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Inserting a metallic $\\mathrm{SrVO_3}$ layer that screens interfacial phonons lowered the pairing temperature to about 48 K (Guo et al., Nano Letters, 2024, arXiv 2407.09880), supporting a role for interfacial electron-phonon coupling.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fese-sto-interface.ktao3-orientation",
      "fields": {
        "title": {
          "text": "Why does $\\mathrm{KTaO_3}$ interface superconductivity depend on crystal orientation?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Electron gases at the surface of $\\mathrm{KTaO_3}$ superconduct at about $2\\,\\mathrm{K}$ on one crystal face and at much lower temperature, or not at all, on another, which no simple theory explains.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Two-dimensional electron gases at EuO/$\\mathrm{KTaO_3}$ and $\\mathrm{LaAlO_3}$/$\\mathrm{KTaO_3}$ interfaces superconduct with $T_c \\sim 2\\,\\mathrm{K}$ for (111) and $\\sim 1\\,\\mathrm{K}$ for (110) orientation (2021), while (001) interfaces show much lower or no $T_c$. Identify the pairing interaction and the origin of the orientation dependence, for example coupling to soft transverse-optic phonons that symmetry allows only for some orientations.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fese-sto-interface.pairing-symmetry",
      "fields": {
        "title": {
          "text": "Pairing symmetry of monolayer FeSe on $\\mathrm{SrTiO_3}$",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "With only electron pockets at $M$, candidate states are plain s-wave (phonon-assisted), nodeless d-wave (sign change between the two electron pockets), incipient $s\\pm$ (pairing involving a hole band below $E_F$) and states with interband pairing. Determine the relative sign of the gap on the two electron pockets and whether it varies between the two Fe sublattices.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fese-sto-interface.replica-band-origin",
      "fields": {
        "precise": {
          "text": "Lee et al. (2014) observed replica bands offset by $\\sim 100\\,\\mathrm{meV}$, interpreted as $q \\sim 0$ electron-phonon coupling with $\\mathrm{SrTiO_3}$ phonons; Li and Sawatzky (2018) proposed extrinsic energy loss of photoelectrons. Determine whether the replicas are intrinsic spectral weight of the FeSe electrons and, if so, the coupling constant they imply.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fese-sto-interface.transport-tc",
      "fields": {
        "title": {
          "text": "What is the zero-resistance transition temperature of monolayer FeSe on $\\mathrm{SrTiO_3}$?",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Ex situ transport on capped monolayers gives onset $T_c \\sim 40\\,\\mathrm{K}$ with lower zero-resistance temperatures, diamagnetic (Meissner) onset appears near 65 K (Zhang et al., Science Bulletin 60, 1301, 2015), photoemission gap closing occurs near 55-65 K, and one in situ four-probe study reported $T_c$ above 100 K (Ge et al. 2015) that has not been reproduced. Determine the onset and zero-resistance $T_c$ of uncapped monolayer FeSe/$\\mathrm{SrTiO_3}$ in situ, and whether the gap-closing temperature marks phase coherence or only pairing.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Nernst measurements on ultrathin FeSe/$\\mathrm{SrTiO_3}$ find superconducting fluctuations only below about 1.2 times the onset $T_c$ and suggest the gap seen above $T_c$ in photoemission may have a non-superconducting origin (Kobayashi, Ogawa and Maeda, Physical Review B 112, 094525, 2025).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.flat-band-geometry.linear-tc-scaling",
      "fields": {
        "precise": {
          "text": "For an isolated flat band of width $W \\ll U$ ($U$ the effective attraction), mean-field and Berezinskii-Kosterlitz-Thouless theory predict $T_c \\sim U$ times a band-geometric factor, compared with $T_c \\sim W \\exp(-1/(N(0) U))$ in dispersive bands, $N(0)$ the density of states. Determine whether $T_c$ scales linearly with $U$ in a moire flat-band superconductor where the interaction is tuned, for example by gate-screening distance or dielectric environment. An answer is the measured exponent of $T_c$ versus $U$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.floquet-dtc.mbl-dtc-stability",
      "fields": {
        "title": {
          "text": "Is the many-body-localized time crystal a stable phase?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.floquet-dtc.prethermal-dtc-short-range",
      "fields": {
        "precise": {
          "text": "For a periodically driven spin lattice with short-range couplings of strength $J$, drive frequency $\\omega >> J/\\hbar$ and near-$\\pi$ spin flips, prethermal theory (Else, Bauer, Nayak, PRX 7, 011026, 2017) predicts period-doubled response lasting $t* \\sim \\mathrm{exp}(c \\hbar \\omega/J)$; at finite energy density this needs spontaneous breaking of an emergent Ising symmetry of the prethermal Hamiltonian, hence $d \\ge 2$ for short-range couplings. Does a $d = 2$ short-range system show t* growing exponentially with $\\omega$, and does the response vanish above the critical energy density of the prethermal Ising transition? Answer yes or no, with $t*(\\omega)$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fractional-chern-insulators.anyon-charge-zero-field",
      "fields": {
        "precise": {
          "text": "In twisted $\\mathrm{MoTe_2}$ or rhombohedral graphene FQAH states at $\\nu = 2/3$ and $B = 0$, measure the quasiparticle charge $e*$ from the shot-noise Fano factor at a quantum point contact or from Fabry-Perot interference periods, and the braiding phase $2\\pi/3$ by interferometry. An answer is $e*/e$ and the braiding phase with uncertainties.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fractional-chern-insulators.anyon-superconductivity",
      "fields": {
        "plain": {
          "text": "Adding a few extra electrons to a fractional state may produce a superconductor whose carriers are anyons, and the superconductivity seen next to fractional states in twisted $\\mathrm{MoTe_2}$ could be the first example.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Theory (Z. D. Shi and T. Senthil, arXiv:2409.20567, 2024) proposed that doping a $\\nu = 2/3$ fractional Chern insulator can yield a chiral topological superconductor from anyon pairing. Determine whether the superconductivity observed near FQAH states in twisted $\\mathrm{MoTe_2}$ (2025) is of this type, using its predicted signatures: a specific chiral central charge, a charge-$2e$ condensate breaking time reversal, and a $T_{\\mathrm{c}}$ and superfluid stiffness that grow from zero with doping away from the fractional state. An answer is yes or no with the matching signatures.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.fractional-chern-insulators.geometry-criterion",
      "fields": {
        "precise": {
          "text": "For a partially filled isolated Chern band ($C=1$) of width $W$ with Coulomb scale $U=e^2/(\\epsilon a_M)$, Berry curvature $\\Omega(k)$ and quantum metric $g(k)$, determine the boundary between the $\\nu=1/3$ and $2/3$ fractional Chern insulators and competing charge-density-wave or Fermi-liquid states as a function of $W/U$, the Berry-curvature variance, and the trace-condition violation $T = (1/2 \\pi) \\int \\mathrm{d}^{2}k [\\mathrm{tr}\\,g(k) - \\left| \\Omega(k) \\right|]$. An answer is a phase diagram validated by exact diagonalization or DMRG across twisted $\\mathrm{MoTe_2}$, rhombohedral graphene and model bands.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.frustrated-heisenberg.er2ti2o7-selection",
      "fields": {
        "title": {
          "text": "Quantum order by disorder or virtual crystal-field selection in $\\mathrm{Er_2Ti_2O_7}$?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{Er_2Ti_2O_7}$ orders into one particular spin pattern although its main interactions treat a whole continuous family equally. Both quantum fluctuations and virtual excitations to higher atomic energy levels can pick that pattern, and their relative share is unsettled.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{Er_2Ti_2O_7}$ with anisotropic nearest-neighbor exchange $(J_{zz}, J_{pm}, J_{pmpm}, J_{zpm})$ fitted to neutron data, compute the energy splitting between the $\\psi_2$ and $\\psi_3$ states and the pseudo-Goldstone gap produced by (a) quantum zero-point fluctuations within the ground doublet and (b) virtual crystal-field excitations, and compare with the measured gap. An answer gives the fraction of the measured gap due to each mechanism.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.frustrated-heisenberg.spin-nematic-observation",
      "fields": {
        "precise": {
          "text": "In a frustrated J1-J2 magnet with J1 < 0 (candidate $\\mathrm{LiCuVO_4}$ near saturation) or a spin-1 magnet with bound two-magnon states (candidate Na2BaNi(PO4)2), demonstrate quadrupolar order $\\langle S^{+}_{i}S^{+}_{j}\\rangle \\ne 0$ with $\\langle S_{i}\\rangle=0$ using a direct probe (resonant x-ray scattering, NMR lineshape and relaxation, or two-magnon bound-state spectroscopy). An answer is a material and field range with a measured quadrupolar order parameter.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Evidence in $\\mathrm{LiCuVO_4}$ near saturation remains indirect (NMR, magnetization, magnetostriction); condensation of a two-magnon bound state was reported in spin-1 Na2BaNi(PO4)2 (Sheng et al., Research Square preprint 2024) without a direct measurement of the quadrupolar order parameter.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.halide-perovskites.defect-tolerance",
      "fields": {
        "precise": {
          "text": "In MAPbI3, FAPbI3 and $\\mathrm{CsPbBr_3}$, nonradiative lifetimes reach about $10^{-6}$ s at trap densities of order $10^{15}\\ \\text{to}\\ 10^{16}\\,\\mathrm{cm}^{-3}$ despite modest mobilities. Determine which mechanism dominates the suppression of Shockley-Read-Hall (defect-mediated) recombination: shallow intrinsic defect levels from antibonding valence-band character, large-polaron screening of capture, dynamic disorder reducing capture cross sections, or spin-split (Rashba) band edges. An answer is a ranking of mechanisms with first-principles nonadiabatic capture rates matching measured lifetimes versus $T$ and composition.",
          "how": [
            "inside:e-notation",
            "outside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.halide-perovskites.hot-carrier-cooling",
      "fields": {
        "precise": {
          "text": "At excitation densities above about $10^{18}\\,\\mathrm{cm}^{-3}$, hot-carrier cooling in MAPbI3 and $\\mathrm{CsPbBr_3}$ slows from about 0.3 ps to tens or hundreds of ps. Separate the contributions of the hot-phonon bottleneck (slow decay of longitudinal-optical phonons), Auger reheating, and large-polaron screening, and determine whether any slowdown persists below $10^{17}\\,\\mathrm{cm}^{-3}$, the density under sunlight. An answer is quantified cooling-time contributions versus density and temperature.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.halide-perovskites.ion-migration",
      "fields": {
        "title": {
          "text": "Which ions migrate in operating perovskite devices and why?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.halide-perovskites.nanocrystal-blinking",
      "fields": {
        "precise": {
          "text": "Single CdSe, CdSe/CdS and $\\mathrm{CsPbBr_3}$ nanocrystals show on and off duration distributions $P(t) \\sim t^{-\\alpha}$ with $\\alpha \\sim 1.5$ over about six decades, plus partially bright grey states. Determine the microscopic mechanism (Auger quenching in charged nanocrystals, hot-carrier trapping with fluctuating rates, diffusing energy levels of surface traps) that yields the power law and its exponent, consistent with photon statistics, lifetime-intensity correlations and suppression in thick-shell structures. An answer is a mechanism reproducing $P(t)$ and its dependence on excitation intensity.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.halide-perovskites.rashba-recombination",
      "fields": {
        "title": {
          "text": "Does dynamic Rashba splitting slow radiative recombination in perovskites?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Inversion-breaking lattice fluctuations in MAPbI3 could produce a dynamic Rashba splitting that offsets the band extrema in momentum and lowers the bimolecular radiative coefficient $B$ (measured of order $10^{-10}\\,\\mathrm{cm}^3/\\mathrm{s}$). Determine the size of the room-temperature splitting (static or dynamic, in meV) and its effect on $B$, with photon recycling separated out. An answer is the splitting value and the fractional change of $B$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermion-sc.cecu2si2-gap",
      "fields": {
        "title": {
          "text": "Order parameter of the fully gapped heavy-fermion superconductor $\\mathrm{CeCu_2Si_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{CeCu_2Si_2}$, the first heavy-fermion superconductor (1979), was long believed to have a gap vanishing along lines on the Fermi surface, but measurements since 2014 show a full gap, which a simple d-wave state cannot produce.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine the superconducting order parameter of $\\mathrm{CeCu_2Si_2}$ ($T_{c} \\sim 0.6\\,\\mathrm{K}$) consistent with: activated specific heat and penetration depth below $\\sim 0.1\\,\\mathrm{K}$ (Kittaka et al., PRL 2014), insensitivity of $T_{c}$ to electron-irradiation disorder (Takenaka et al., PRL 2017), the absence of a Hebel-Slichter peak in NMR $1/T_{1}$, and a neutron spin resonance. Candidates: $s\\pm$ between heavy and light bands, $d+d$ band-mixing pairing, and sign-preserving s++. An answer is one state fitting all these data, plus a phase-sensitive or impurity-state test that separates sign-changing from sign-preserving gaps.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermion-sc.cerh2as2-two-phases",
      "fields": {
        "title": {
          "text": "Nature of the two superconducting phases of $\\mathrm{CeRh_2As_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "In $\\mathrm{CeRh_2As_2}$ a magnetic field along one crystal axis switches the superconductor from one state to another, possibly from even-parity to odd-parity pairing, made possible because each cerium layer lacks a center of inversion although the whole crystal has one.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "$\\mathrm{CeRh_2As_2}$ ($T_{c} \\sim 0.26\\ \\mathrm{K}$) shows for $H \\mid\\mid c$ a transition at $H* \\sim 40 \\mathrm{kG}$ between a low-field phase SC1 and a high-field phase SC2 extending to $H_c2 \\sim 140 \\mathrm{kG}$ (Khim et al., Science 2021). Determine whether SC1 and SC2 are the even- and odd-parity states of locally noncentrosymmetric Ce layers, or whether $H*$ is controlled by the quadrupole-density-wave or antiferromagnetic order found near or inside the superconducting phase. An answer identifies the order parameters of both phases by site-resolved NMR Knight shift, field-angle dependence of $H*$, and the relation of $H*$ to the normal-state order.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermion-sc.ute2-field-reentrance",
      "fields": {
        "title": {
          "text": "Mechanism of field-reentrant superconductivity in $\\mathrm{UTe_2}$ above 400 kG",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "In $\\mathrm{UTe_2}$, superconductivity reappears in magnetic fields of about 400 to 650 kG when the field is tilted at a particular angle, fields far above those that destroy ordinary superconductors.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{UTe_2}$ with the field tilted from the b axis toward c by roughly 20 to 40 degrees, superconductivity reappears above the metamagnetic transition $H_m \\sim 350\\,\\mathrm{kG}$ and survives to $\\sim 650\\,\\mathrm{kG}$ (Ran et al., Nature Physics 2019). Determine the pairing mechanism and order parameter of this field-polarized phase: triplet pairing mediated by field-enhanced ferromagnetic fluctuations, compensation of the exchange field by the applied field (Jaccarino-Peter mechanism), or pairing on a Fermi surface reconstructed at $H_m$. An answer predicts the angular window and the upper critical field from a model with independently measured parameters.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermion-sc.ute2-order-parameter",
      "fields": {
        "title": {
          "text": "Symmetry of the superconducting order parameter of $\\mathrm{UTe_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{UTe_2}$ is a heavy-fermion superconductor whose electron pairs probably have parallel spins (spin-triplet), but the exact pairing pattern is still argued over.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine the irreducible representation of the superconducting order parameter of orthorhombic $\\mathrm{UTe_2}$ (point group D2h; candidates B3u, B2u, Au, or multicomponent combinations) at ambient pressure and zero field, including node positions and whether time-reversal symmetry is broken. An answer is a set of measurements (Knight shift along a, b, c; directional thermal conductivity; polar Kerr; quasiparticle interference of surface states) consistent with one representation.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermions.kondo-breakdown-vs-sdw",
      "fields": {
        "precise": {
          "text": "For heavy-fermion quantum critical points (CeCu6-xAux, $\\mathrm{YbRh_2Si_2}$, $\\mathrm{CeRhIn_5}$ under pressure, $\\mathrm{CeCoIn_5}$), determine whether criticality is of Hertz-Millis-Moriya spin-density-wave type with Kondo screening intact, or of local (Kondo breakdown) type in which the f electrons leave the Fermi volume at the critical point. An answer classifies the known materials using $\\omega/T$ scaling of the dynamical spin susceptibility, the Fermi-volume change, and the exponents of $C/T$ and $\\rho(T)$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermions.kondo-insulator-neutral-fermions",
      "fields": {
        "title": {
          "text": "Do Kondo insulators host charge-neutral fermions with a Fermi surface?",
          "how": [
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Some insulators built from heavy-fermion elements, such as $\\mathrm{YbB_{12}}$ and $\\mathrm{SmB_6}$, show metal-like signatures, heat conduction by mobile carriers and quantum oscillations, while not conducting electricity; this would require particles that carry heat but no charge.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether a finite residual thermal conductivity $\\kappa_{xx}/T$ at $T \\to 0$ and bulk quantum oscillations in insulating Kondo insulators ($\\mathrm{YbB_{12}}$, $\\mathrm{SmB_6}$) arise from charge-neutral fermions with a Fermi surface (Majorana or composite-exciton Fermi seas) or from phonons, magnetic impurities and metallic inclusions. An answer is field-dependent $\\kappa_{xx}/T$ and specific heat $\\gamma$ on crystals with controlled impurity content, compared with a theory that predicts their magnitudes.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Sato et al. (Nature Physics 2019) reported finite $\\kappa/T$ at $T \\to 0$ in $\\mathrm{YbB_{12}}$; for $\\mathrm{SmB_6}$, Hartstein et al. (2018) attributed field-dependent heat transport to neutral fermions and Boulanger et al. (2018) to phonons scattered by magnetic impurities.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermions.smb6-topological-surface",
      "fields": {
        "title": {
          "text": "Is $\\mathrm{SmB_6}$ a topological Kondo insulator?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "$\\mathrm{SmB_6}$ conducts on its surface while its interior insulates at low temperature; theory predicts these surface states are topological, meaning protected by symmetry and band structure, but this is not settled.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether the conducting surfaces of $\\mathrm{SmB_6}$ are protected by the time-reversal Z2 invariant from $f-d$ band inversion at the $X$ points, with an odd number of Dirac cones, or are trivial polar-surface states. An answer is spin-resolved ARPES and transport (weak antilocalization, thickness independence) on several crystal faces, consistent with a Z2 index computed from the bulk bands.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermions.uru2si2-hidden-order",
      "fields": {
        "title": {
          "text": "What is the order parameter of hidden order in $\\mathrm{URu_2Si_2}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Below 17.5 K, $\\mathrm{URu_2Si_2}$ enters an ordered phase that releases a large amount of entropy, yet nearly forty years of experiments have not identified what orders.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Identify the order parameter of the phase below $T_{\\mathrm{HO}} = 17.5\\ \\mathrm{K}$ in $\\mathrm{URu_2Si_2}$, which has no ordered magnetic moment of matching size and doubles the unit cell along c (wavevector $(0,0,1)$). Candidates include higher-rank multipoles (hexadecapole, dotriacontapole), hastatic order and chirality density waves. An answer gives the symmetry (irreducible representation) and microscopic character, confirmed by a probe that couples directly to it (resonant x-ray scattering, Raman, NMR).",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Raman data (2015) show an $A_2g$ mode suggesting chirality-density-wave order, while reports of in-plane fourfold symmetry breaking disagree between probes.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.heavy-fermions.ybrh2si2-fermi-jump",
      "fields": {
        "title": {
          "text": "Does the Fermi volume of $\\mathrm{YbRh_2Si_2}$ jump at its critical field?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Hall-effect data suggest that the number of electrons in the Fermi sea of $\\mathrm{YbRh_2Si_2}$ changes abruptly at a critical magnetic field when cooled to zero temperature.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{YbRh_2Si_2}$ at $T \\to 0$ across the critical field $B_c \\sim 600\\,\\mathrm{G}$ (field in the ab plane), determine whether the Fermi volume changes discontinuously from large (including the 4f hole) to small, as inferred from the Hall crossover whose width scales with $T$. An answer is a $T = 0$ extrapolation of the crossover width of Fermi-volume-sensitive transport (Hall coefficient, thermopower) in crystals with residual resistivity ratio of order 100 or more, or a Fermi-surface measurement at fields close to $B_c$, for example on chemically substituted samples whose critical field lies in the range accessible to quantum oscillations.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.helium3-quantum-solids.2d-3he-spin-liquid",
      "fields": {
        "title": {
          "text": "Is second-layer 3He on graphite a gapless spin liquid?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "At the $4/7$ commensurate density of the 2D solid 3He layer on preplated graphite, multiple-spin ring exchange on a triangular lattice produces no magnetic order: magnetization measured by direct nuclear demagnetization rises smoothly down to about $10^{-5}\\,\\mathrm{K}$, which bounds any spin gap below about $10^{-5}\\,\\mathrm{K}$ (Masutomi et al. 2004). Determine the ground state of the triangular ring-exchange model at the measured $J2, J4, J5, J6$ ratios and test experimentally whether the state is a gapless spin liquid, gapped, or ordered. An answer is a classification supported by both computation and data below $10^{-5}\\,\\mathrm{K}$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Heat capacity and susceptibility below $10^{-5}$ K together with a controlled numerical solution of the ring-exchange model at the measured couplings.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.helium3-quantum-solids.ab-nucleation",
      "fields": {
        "precise": {
          "text": "For the first-order A-B transition, homogeneous nucleation with the measured interface tension gives a critical radius of order $10^{-4}$ cm and a barrier of order $10^{6} k_B T$, so rates of order $\\exp(-10^{6})$. Identify the actual nucleation mechanism (local heating by cosmic rays in the 'Baked Alaska' scenario, resonant tunneling between phases, nucleation at surfaces, textures or impurities) and predict supercooling statistics versus pressure, field and cell geometry. An answer is a mechanism quantitatively reproducing measured supercooling distributions.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.helium3-quantum-solids.slab-modulated-phase",
      "fields": {
        "precise": {
          "text": "In $3\\mathrm{He}$ confined to slabs of thickness $D \\sim 10^{-4}\\,\\mathrm{cm}$ with pair-breaking walls, quasiclassical theory predicts a stripe phase (Vorontsov and Sauls 2007) of periodic domain walls in a planar-distorted B order parameter, between the A and B phases. Determine whether a modulated phase exists, its period and its region in $\\left(D, P, T\\right)$, and distinguish a stripe phase from a pair-density-wave state and from a polar-distorted B phase with pinned domain walls. An answer is a phase diagram with direct evidence of the modulation.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "NMR in a $1.1 \\times 10^{-4}$ cm slab (Levitin et al. 2019) gave evidence for a stripe phase; a nanofluidic resonator experiment (Shook et al. 2020) claimed a pair-density-wave state, and a 2020 Comment by Levitin et al. disputed that interpretation.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hubbard-mott.pure-model-sc",
      "fields": {
        "title": {
          "text": "Does the pure square-lattice Hubbard model superconduct at moderate doping?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hydrides.ambient-pressure-hydride",
      "fields": {
        "title": {
          "text": "Is there a hydride superconducting above 77 K at ambient pressure?",
          "how": [
            "title:question-mark"
          ]
        },
        "status_note": {
          "text": "Calculations (2024) predicted $\\mathrm{Mg_2IrH_6}$ with $T_{c}$ above $100\\,\\mathrm{K}$ at ambient pressure; no superconducting sample has been reported.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hydrides.eliashberg-predictive",
      "fields": {
        "title": {
          "text": "Can first-principles Eliashberg theory predict hydride $T_{c}$ within ten percent?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Determine whether Migdal-Eliashberg theory with first-principles electron-phonon coupling, including quantum anharmonic lattice dynamics and zero-point motion and with $\\mu*$ computed or fixed in advance, predicts $T_{c}$ of compressed hydrides ($\\mathrm{H_3S}$, $\\mathrm{LaH_{10}}$, $\\mathrm{CaH_6}$, $\\mathrm{YH_6}$) within 10 percent and their isotope coefficients. An answer is a blind prediction later confirmed or refuted by experiment.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Calculations reproduce $T_{c}$ of $\\mathrm{H_3S}$ and $\\mathrm{LaH_{10}}$ approximately, but results depend on $\\mu*$ and on the treatment of anharmonicity.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hydrides.la-sc-h-room-temperature",
      "fields": {
        "title": {
          "text": "Is 298 K superconductivity in compressed La-Sc-H reproducible?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Song et al. (arXiv 2510.01273, 2025) report onset $T_c = 271\\ \\text{to}\\ 298\\,\\mathrm{K}$ at $1.95\\ \\text{to}\\ 2.66\\,\\mathrm{Mbar}$ in hexagonal $\\mathrm{LaSc_2H_{24}}$, synthesized by laser heating La-Sc alloy with ammonia borane in diamond anvil cells, with zero resistance, field suppression of $T_c$ and synchrotron diffraction. Determine whether independent groups reproduce $T_c$ above $270\\,\\mathrm{K}$ in the same structure, and whether magnetic signatures (flux expulsion, trapped flux) and the isotope coefficient agree with Eliashberg predictions for $\\mathrm{LaSc_2H_{24}}$. An answer is independent replication with magnetic data, or failure to reproduce under the stated synthesis.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "Independent synthesis of $\\mathrm{LaSc_2H_{24}}$ with resistive and magnetic transitions above 270 K at a calibrated pressure, plus a deuterium isotope measurement.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hydrides.magnetic-evidence",
      "fields": {
        "title": {
          "text": "Do megabar hydrides show consistent bulk magnetic evidence of superconductivity?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{H_3S}$ and $\\mathrm{LaH_{10}}$ at $\\sim 1.5 \\text{ to } 1.9 \\mathrm{Mbar}$, establish bulk magnetic signatures (flux expulsion, trapped flux, penetration depth $\\lambda_L$, critical current) that agree quantitatively with the resistive transitions and with the Ginzburg-Landau parameters implied by $H_c2$. An answer is a magnetic measurement reproduced by independent groups with consistent volume fraction and $\\lambda_L$.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Independent replication of magnetization or local magnetometry on $\\mathrm{H_3S}$ or $\\mathrm{LaH_{10}}$ with quantitative agreement among volume fraction, $\\lambda_L$ and $H_c2$.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Nitrogen-vacancy magnetometry imaging of flux expulsion in a cerium hydride (2024) and tunneling measurement of a gap near $60\\,\\mathrm{meV}$ in $\\mathrm{H_3S}$ (2025) support superconductivity; some magnetization data sets remain disputed.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.hydrides.metallic-hydrogen-tc",
      "fields": {
        "title": {
          "text": "Does metallic hydrogen superconduct, and at what temperature?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.insulator-quantum-oscillations.inas-gasb-gap-oscillations",
      "fields": {
        "plain": {
          "text": "Quantum wells of InAs and GaSb form an insulator whose small energy gap comes from mixing of electron and hole bands, yet their conductance oscillates in a magnetic field when the electron density is tuned into the gap. Whether this is the band-mixing mechanism proposed for $\\mathrm{SmB_6}$ or something else is unknown.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.insulator-quantum-oscillations.oscillation-mechanism",
      "fields": {
        "precise": {
          "text": "Candidates are Landau quantization of hybridized bands with a small inverted gap, which gives magnetization oscillations at the frequency of the unhybridized Fermi surface (Knolle and Cooper 2015); emergent neutral fermions with a Fermi surface (spinons, composite excitons, Majorana Fermi sea); and in-gap impurity bands or metallic inclusions. An answer predicts the frequency, the amplitude temperature dependence including deviations from Lifshitz-Kosevich form, and which quantities oscillate (magnetization, resistivity, heat capacity, thermopower) in $\\mathrm{SmB_6}$, $\\mathrm{YbB_{12}}$ and monolayer $\\mathrm{WTe_2}$.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "Amplitude versus temperature and gap size in a tunable system (pressure-tuned $\\mathrm{YbB_{12}}$, gate-tuned $\\mathrm{WTe_2}$ or InAs/GaSb wells) where the candidate theories make distinct predictions.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.insulator-quantum-oscillations.smb6-bulk-oscillations",
      "fields": {
        "title": {
          "text": "Are the bulk quantum oscillations in $\\mathrm{SmB_6}$ intrinsic?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Some $\\mathrm{SmB_6}$ crystals show magnetization oscillations typical of metal electrons although their resistance says the bulk is insulating. Other groups attribute the oscillations to surface states or to aluminum inclusions left from crystal growth.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In the Kondo insulator $\\mathrm{SmB_6}$, de Haas-van Alphen oscillations were reported as two-dimensional surface signals (Li et al. 2014) and as three-dimensional bulk signals with large Fermi surfaces and anomalous low-temperature amplitude growth (Tan et al. 2015, floating-zone crystals); in flux-grown crystals oscillations were traced to embedded Al (2018-2019). Determine whether bulk oscillations exist in stoichiometric, inclusion-free $\\mathrm{SmB_6}$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.insulator-quantum-oscillations.wte2-insulating-landau",
      "fields": {
        "title": {
          "text": "What carries Landau quantization in insulating monolayer $\\mathrm{WTe_2}$?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Monolayer $\\mathrm{WTe_2}$, an insulator in its interior, shows resistance oscillations starting at a weak magnetic field, as if it contained very mobile particles. What these particles are is unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In gated monolayer $\\mathrm{WTe_2}$ near charge neutrality, where the bulk is insulating (a 2D topological insulator, also proposed as an excitonic insulator), resistance oscillates periodically in $1/B$ from an onset of $\\sim 5 \\times 10^{3}\\,\\mathrm{G}$ (Wang et al. 2021), and thermopower oscillates with sign changes (2024). Identify the mobile fermions responsible (neutral fermions, excitons, or charged carriers of a hidden Fermi surface) and explain why oscillations appear while the bulk resistance stays large.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.insulator-quantum-oscillations.ybb12-neutral-fermions",
      "fields": {
        "title": {
          "text": "Does insulating $\\mathrm{YbB_{12}}$ host a Fermi surface of neutral fermions?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{YbB_{12}}$ shows oscillations in resistance and magnetization, plus heat capacity and heat conduction that grow linearly with temperature as in a metal, while remaining electrically insulating.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{YbB_{12}}$, quantum oscillations in resistivity and magnetization appear in the insulating state above $\\sim 3.5 \\times 10^{5}\\,\\mathrm{G}$ (Xiang et al. 2018), heat-capacity oscillations with frequency $\\sim 6.7 \\times 10^{6}\\,\\mathrm{G}$ were reported in 2025, and zero-field specific heat and thermal conductivity have linear-in-$T$ terms (Sato et al. 2019). Determine whether these signals come from a bulk Fermi surface of charge-neutral fermions.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.iron-based.bogoliubov-fermi-surface",
      "fields": {
        "title": {
          "text": "Does tetragonal FeSe1-xSx host Bogoliubov Fermi surfaces?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.iron-based.gap-sign-electron-pockets",
      "fields": {
        "precise": {
          "text": "For monolayer FeSe on $\\mathrm{SrTiO_3}$, (Li,Fe)OHFeSe and KxFe2-ySe2, which lack hole pockets at $\\Gamma$, determine whether the gap changes sign between the electron pockets at $M$ (d-wave or bonding-antibonding $s\\pm$) or is sign-preserving ($s++$). An answer is a phase-sensitive test, such as quasiparticle interference with magnetic and nonmagnetic defects or defect-bound in-gap states, with unambiguous sign assignment.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.iron-based.nematic-driving-force",
      "fields": {
        "title": {
          "text": "What drives electronic nematic order in iron-based superconductors?",
          "how": [
            "title:question-mark"
          ]
        },
        "settled_by": {
          "text": "A calculation reproducing $T_s$, the orbital splitting and the spin-fluctuation spectrum of FeSe and $\\mathrm{BaFe_2As_2}$ with one set of interaction parameters.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.iron-based.nematic-tc-enhancement",
      "fields": {
        "title": {
          "text": "Do nematic quantum critical fluctuations enhance $T_c$?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.iron-based.s-pm-sign-change",
      "fields": {
        "title": {
          "text": "Does the gap change sign between hole and electron pockets?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kagome-metals.cdw-mechanism",
      "fields": {
        "title": {
          "text": "Is the kagome charge-density wave electronic or phonon driven?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kagome-metals.cdw-trsb",
      "fields": {
        "title": {
          "text": "Does the charge order in $\\mathrm{CsV_3Sb_5}$ break time-reversal symmetry?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Some experiments suggest that the charge order in $\\mathrm{CsV_3Sb_5}$ comes with tiny circulating electric currents (loop currents) that break time-reversal symmetry, while sensitive optical tests see nothing.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether the $2x2$ charge-density-wave state of $\\mathrm{CsV_3Sb_5}$ ($T_{\\mathrm{CDW}} = 94\\,\\mathrm{K}$) breaks time-reversal symmetry, as in loop-current (chiral flux) phases. Reconcile muSR and field-trained transport and optical signals with high-resolution polar Kerr data and spin-polarized STM that found no signal. An answer is a symmetry-resolved measurement on the same crystals with sensitivity sufficient to detect the orbital moments predicted by loop-current theory.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kagome-metals.cscr3sb5-pairing",
      "fields": {
        "title": {
          "text": "Density-wave order and pairing in pressurized $\\mathrm{CsCr_3Sb_5}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "$\\mathrm{CsCr_3Sb_5}$, a chromium kagome metal, forms a density wave at normal pressure and becomes a superconductor near 6 K when squeezed, next to a metal whose resistance is linear in temperature; what the density wave is and whether its fluctuations pair the electrons is unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "At ambient pressure $\\mathrm{CsCr_3Sb_5}$ undergoes a coupled charge and spin density-wave transition at about 50 to 60 K; under pressure of roughly 40 kbar and above it is suppressed, superconductivity with $T_{c}$ up to $\\sim 6\\,\\mathrm{K}$ appears, and the normal state shows non-Fermi-liquid resistivity (Liu et al., Nature 2024). Identify the density-wave order (wavevector, moment arrangement, altermagnetic or not) and determine whether its quantum critical fluctuations drive pairing. An answer is a refined magnetic structure and pressure phase diagram from neutron scattering, muSR or NMR under pressure, plus a gap-symmetry measurement in the superconducting phase.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kagome-metals.pdw-csv3sb5",
      "fields": {
        "title": {
          "text": "Is there a pair density wave in superconducting $\\mathrm{CsV_3Sb_5}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Tunneling microscopy saw the superconducting gap of $\\mathrm{CsV_3Sb_5}$ oscillate in space with a new period, which could be a pair density wave or a side effect of the charge order.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether the $4a/3$ spatial modulation of the superconducting gap reported by STM in $\\mathrm{CsV_3Sb_5}$ (2021) is an independent pair-density-wave order parameter or a modulation of the uniform condensate induced by the charge-density wave. An answer is a test of whether the modulation survives when the charge order is suppressed or changed (by pressure or substitution) and whether it has its own phase coherence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kitaev-materials.cobaltate-kitaev-exchange",
      "fields": {
        "plain": {
          "text": "Theory in 2018 proposed that cobalt honeycomb compounds could realize the Kitaev model with weaker competing couplings than the ruthenium and iridium ones. Neutron studies of BaCo2(AsO4)2 instead fit simpler models without large Kitaev terms, and the magnetic pattern of $\\mathrm{Na_2Co_2TeO_6}$ is itself debated.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{Na_2Co_2TeO_6}$, $\\mathrm{Na_3Co_2SbO_6}$ and BaCo2(AsO4)2 (Co2+ d7 pseudospin-1/2 on honeycomb lattices), determine $|K|/\\max(|J1|, |J3|, |\\Gamma|)$ from fits of the full magnon spectra, and for $\\mathrm{Na_2Co_2TeO_6}$ whether the zero-field order is single-q zigzag in three domains or a triple-q state. An answer gives the exchange set with error bars per compound and the ordering-wavevector content.",
          "how": [
            "inside:operator-word",
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Halloran et al. (PNAS 2023) fit BaCo2(AsO4)2 with an XXZ $J1-J3$ model with small Kitaev terms, while Kruger et al. (PRL 2023) argued for triple-q order in $\\mathrm{Na_2Co_2TeO_6}$ near a hidden-$\\mathrm{SU}(2)$-symmetric point.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kitaev-materials.half-quantized-plateau",
      "fields": {
        "status_note": {
          "text": "Reported by Kasahara et al. (Nature 2018) and Yokoi et al. (Science 2021); Bruin et al. (Nature Physics 2022) found $\\kappa_{xy}/T$ near the half-quantized value over an extended region but without a strict plateau; Czajka et al. (Nature Materials 2023) found a strongly $T$-dependent $\\kappa_{xy}/T$ and attributed it to topological magnons.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kitaev-materials.intermediate-field-phase",
      "fields": {
        "precise": {
          "text": "For in-plane fields between the zigzag critical field $H_c1$ (about 70 to 80 kOe) and full polarization, determine whether a distinct thermodynamic phase bounded by phase transitions (in specific heat, magnetocaloric effect, magnetostriction) exists, whether its excitations form a fractionalized continuum or multi-magnon bound states, and whether the oscillatory features of $\\kappa_{xx}(H)$ at $T < 1\\ \\mathrm{K}$ in this window mark intrinsic transitions or shifted phase boundaries of stacking inclusions. An answer is a phase diagram with identified boundaries and a classification of the intermediate state.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Thermodynamic measurements resolving or excluding a second transition above $H_c1$ on stacking-controlled crystals, combined with neutron and THz spectra fitted by a calibrated spin model.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kitaev-materials.rucl3-spin-hamiltonian",
      "fields": {
        "precise": {
          "text": "Determine the exchange constants of alpha-RuCl3 in $H = \\sum$ over nearest-neighbor bonds $\\langle ij\\rangle$ of type $\\gamma$ of [$J S_i . S_j + K S^{\\gamma}_{i} S^{\\gamma}_{j} + \\Gamma (S^{\\alpha}_{i} S^{\\beta}_{j} + S^{\\beta}_{i} S^{\\alpha}_{j}) + \\Gamma'$ (terms mixing $\\gamma$ with $\\alpha$ and $\\beta$)] $+ J3 \\sum$ over third neighbors of $S_i . S_j$, with $(\\alpha, \\beta, \\gamma)$ a permutation of $(x, y, z)$, from a joint fit of inelastic neutron spectra, THz and ESR modes, the field-angle dependence of the critical field and the high-field magnon spectrum. An answer is one parameter set with error bars consistent with all these data, including the sign of $K$ and the ratio $K/\\Gamma$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.kitaev-materials.zero-field-kitaev-material",
      "fields": {
        "precise": {
          "text": "Identify a compound with bond-dependent Kitaev exchange $K$ dominant enough over Heisenberg $J$ and off-diagonal $\\Gamma$ terms to lie inside the Kitaev phase of the $J-K-\\Gamma$ model, showing no magnetic order or spin freezing down to $k_{\\mathrm{B}} T << \\mid K \\mid$ and fractionalized excitations confirmed spectroscopically. Candidates include $\\mathrm{H_3LiIr_2O_6}$ (no order but strong disorder) and cobalt-based honeycomb compounds ($\\mathrm{Na_2Co_2TeO_6}$, BaCo2(AsO4)2), whose Kitaev fraction is disputed. An answer is the material with its measured exchange parameters.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.lattice-transport.superdiffusion-under-perturbation",
      "fields": {
        "title": {
          "text": "Does Heisenberg-chain superdiffusion survive symmetric integrability-breaking perturbations?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Take $H = H_{\\mathrm{XXX}} + g V$ with $V$ local, integrability breaking and $\\mathrm{SU}(2)$ invariant (e.g. $V = \\sum_i S_i . S_{i+2}$), at infinite temperature and zero magnetization. De Nardis, Gopalakrishnan, Vasseur, Ware (PRL 127, 057201, 2021) argued that large spin-carrying quasiparticles survive, giving spin conductivity $\\sigma(\\omega) \\sim \\omega^{-1/3}$ at low frequency instead of a finite DC value, while perturbations breaking $\\mathrm{SU}(2)$ restore diffusion. Determine the low-frequency form of $\\sigma(\\omega)$ in the quantum chain, i.e. whether the spin diffusion constant is finite. Answer: finite $D(g)$ or divergent, with the exponent.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.light-induced-sc.k3c60-diamagnetism",
      "fields": {
        "title": {
          "text": "Does photoexcited $\\mathrm{K_3C_{60}}$ above $T_{c}$ expel magnetic field?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Superconductors push out magnetic fields (the Meissner effect). A measurement on light-driven $\\mathrm{K_3C_{60}}$ has so far only set a limit on this effect.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Measure the transient volume susceptibility $\\chi_v$ of $\\mathrm{K_3C_{60}}$ at $T > 20\\ \\mathrm{K}$ after mid-infrared excitation; complete expulsion is $\\chi_v = -1/(4\\pi)$ in CGS, reduced by the excited volume fraction. Answer yes or no: is $\\chi_v(t, T)$ distinguishable from zero within its uncertainty and consistent with superconducting diamagnetism of the excited volume?",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.light-induced-sc.k3c60-transient-state",
      "fields": {
        "title": {
          "text": "What is the photoexcited state of $\\mathrm{K_3C_{60}}$ above $T_{\\mathrm{c}}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "After a mid-infrared pulse, the fulleride $\\mathrm{K_3C_{60}}$ shows an optical response like a superconductor at temperatures far above its normal $20\\ \\mathrm{K}$ transition, lasting up to nanoseconds. What state of matter this is remains unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "$\\mathrm{K_3C_{60}}$ (equilibrium $T_{\\mathrm{c}} = 20\\,\\mathrm{K}$) excited at mid-infrared or terahertz frequencies shows a transient gap in $\\sigma_1(\\omega)$ and $\\sigma_2(\\omega) \\sim 1/\\omega$ well above $T_{\\mathrm{c}}$, with metastable states lasting nanoseconds at high fluence. Identify the state (transient superconductor, fluctuating pairs, high-mobility normal state, or analysis artifact) and its microscopic mechanism. Answer: a mechanism consistent with optical, transport and magnetic data.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.light-induced-sc.metastable-lifetime",
      "fields": {
        "plain": {
          "text": "The state in $\\mathrm{K_3C_{60}}$ survives for nanoseconds, thousands of times longer than the light pulse, which is hard to explain for a driven state. The mechanism of this long life is unknown.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.light-induced-sc.ybco-diamagnetism-replication",
      "fields": {
        "title": {
          "text": "Independent confirmation of transient diamagnetism in driven $\\mathrm{YBa_2Cu_3O_6}$.48",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "In 2024 a group reported that light-driven $\\mathrm{YBa_2Cu_3O_6}$.48 briefly pushes out magnetic field, as a superconductor does. Independent reproduction and other explanations are under discussion.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Fava et al. (Nature 2024) reported a transient diamagnetic response of about 30 percent of complete expulsion after mid-infrared excitation of $\\mathrm{YBa_2Cu_3O_6}$.48 above its equilibrium $T_{c}$, measured by Faraday rotation in an adjacent magneto-optic layer. Does an independent measurement with a different probe reproduce the effect, and can non-superconducting mechanisms (photoinduced magnetization changes, thermal or eddy-current effects) be excluded? Answer yes or no.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magic-angle-graphene.heavy-fermion-picture",
      "fields": {
        "title": {
          "text": "Is magic-angle graphene a topological heavy-fermion system?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Song and Bernevig (PRL 129, 047601, 2022, arXiv:2111.05865) mapped the continuum model of magic-angle twisted bilayer graphene onto localized f-orbitals at AA-stacked regions hybridized with topological dispersive c-electrons. Determine whether experiments at $\\nu = 0\\ \\text{to}\\ \\pm 3$ show the defining features of this picture: Curie-like local-moment susceptibility and moment entropy of order $k_B \\ln 2$ per moire cell at $T \\sim 10\\,\\mathrm{K}$, a coherence temperature below which the moments are screened, and a hybridization gap or Kondo-like resonance in tunnelling at AA sites. An answer is yes or no, based on measured coherence temperature, moment entropy and spectral weight compared with the model parameters.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magnetic-topological-insulators.axion-quasiparticle",
      "fields": {
        "precise": {
          "text": "Li, Wang, Qi and Zhang (Nature Physics, 2010) predicted that in antiferromagnetic topological insulators the axion field $\\theta(r,t)$ acquires dynamics through coupling to the Neel order, giving an axion quasiparticle that hybridizes with photons into axion polaritons under a static magnetic field. Determine whether the polariton exists in a candidate material ($\\mathrm{MnBi_2Te_4}$ family) and measure the axion mass and photon coupling. An answer is spectroscopic detection with the predicted dependence on applied field.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "A 2025 ultrafast-optics study reported coherent axion-mode oscillations in 2D $\\mathrm{MnBi_2Te_4}$; axion-polariton hybridization with light is not observed as of 2026, to this survey's knowledge.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magnetic-topological-insulators.axion-state-mnbi2te4",
      "fields": {
        "title": {
          "text": "Is even-layer $\\mathrm{MnBi_2Te_4}$ an axion insulator?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Thin $\\mathrm{MnBi_2Te_4}$ with an even number of layers shows zero Hall resistance and high longitudinal resistance at zero field, which fits an axion insulator but also an ordinary insulator.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For even-layer $\\mathrm{MnBi_2Te_4}$ in its antiferromagnetic ground state, determine whether $\\theta = \\pi$, with half-quantized surface Hall conductance $\\pm e^{2}/(2h)$ on the top and bottom surfaces, or whether the state is trivial ($\\theta = 0$). The zero Hall plateau alone does not discriminate. An answer is an identification from a surface-resolved or theta-sensitive measurement.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magnetic-topological-insulators.mnbi2te4-surface-gap",
      "fields": {
        "title": {
          "text": "Why the $\\mathrm{MnBi_2Te_4}$ surface Dirac cone appears gapless",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Magnetism should open an energy gap in the surface electrons of $\\mathrm{MnBi_2Te_4}$, which is what allows zero-field quantized Hall effects, but several photoemission experiments see no gap.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Antiferromagnetic $\\mathrm{MnBi_2Te_4}$, whose outermost septuple layer is ferromagnetic, should have an exchange gap of tens of meV in its surface Dirac cone, yet ARPES (Chen et al., PRX 9, 041040, 2019; Nevola et al., PRL 125, 117205, 2020) found a gapless or nearly gapless surface cone, while other studies report gaps. Determine the origin: surface magnetic reconstruction (canted or disordered top layer), Mn-Bi antisite defects, or relocation of the surface state away from the magnetic top layer. An answer links the measured surface magnetic structure to the measured gap on the same samples.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magnetic-topological-insulators.qah-temperature",
      "fields": {
        "precise": {
          "text": "In Cr- or V-doped (Bi,Sb)2Te3 films and odd-layer $\\mathrm{MnBi_2Te_4}$ flakes, full quantum anomalous Hall quantization ($R_{xy} = h/e^2, R_{xx} \\to 0$) appears only at $T$ of order 1 K, while magnetic order sets in at 10-30 K and spectroscopic exchange gaps of tens of meV are reported. Identify the mechanism limiting the quantization temperature (magnetic disorder and gap inhomogeneity, antisite defects, surface-gap fluctuations, parallel bulk conduction) and predict how to raise it. An answer quantitatively links measured disorder to the transport activation gap.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.magnetic-topological-insulators.quantized-magnetoelectric",
      "fields": {
        "precise": {
          "text": "For an axion insulator with $\\theta = \\pi$ (magnetic topological insulator sandwich or even-layer $\\mathrm{MnBi_2Te_4}$), measure the static (dc) magnetoelectric response $P = (\\theta \\alpha / 4\\pi^2) B$ in Gaussian units with $\\alpha = e^2/(\\hbar c)$, i.e., $\\alpha/(4\\pi)$ per unit field at $\\theta = \\pi$, or the equivalent magnetization induced by an electric field. An answer is the measured coefficient in units of $\\alpha/(4\\pi)$ with accuracy better than 10%.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.majorana-zero-modes.nanowire-topological-phase",
      "fields": {
        "title": {
          "text": "Has a semiconductor nanowire reached the topological superconducting phase?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.majorana-zero-modes.shiba-chains",
      "fields": {
        "title": {
          "text": "Are end states of magnetic atom chains on superconductors Majorana modes?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.majorana-zero-modes.vortex-majorana",
      "fields": {
        "title": {
          "text": "Are vortex-core zero modes in FeTeSe Majorana modes?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mbl.heisenberg-chain-existence",
      "fields": {
        "title": {
          "text": "Is the random-field Heisenberg chain localized at strong disorder?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "$H = \\sum_i J S_i . S_{i+1} + h_i S^{z}_i$ with $h_i$ independent and uniform in $[-W, W]$. Does a $W_c < \\infty$ exist such that for $W > W_c$ infinite-temperature eigenstates obey an area law and local memory of the initial state persists as $t \\to \\infty$, in the limit $L \\to \\infty$? Answer yes or no, with an estimate or bound on $W_c$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mbl.many-body-mobility-edge",
      "fields": {
        "title": {
          "text": "Can a many-body mobility edge exist in the thermodynamic limit?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mbl.quasiperiodic-2d",
      "fields": {
        "title": {
          "text": "Is quasiperiodic localization stable in two dimensions?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Interacting bosons or fermions on a square lattice in the quasiperiodic potential $V_i = V [\\cos(2 \\pi \\beta x_i + \\phi_x) + \\cos(2 \\pi \\beta y_i + \\phi_y)]$ with irrational $\\beta$: is there $V_c$ such that local memory persists at infinite time as $L \\to \\infty$? Answer yes or no.",
          "how": [
            "inside:operator-word"
          ]
        },
        "status_note": {
          "text": "Agrawal, Vasseur, Gopalakrishnan (PRB 106, 094206, 2022) argue it is stable in $d=2$ at strong modulation, and a 2025 optical-lattice experiment up to $24 \\times 24$ sites saw no clear size drift of the quasiperiodic crossover.",
          "how": [
            "outside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mbl.two-dimensions-random",
      "fields": {
        "title": {
          "text": "Can random disorder localize an interacting system in two dimensions?",
          "how": [
            "title:question-mark"
          ]
        },
        "status_note": {
          "text": "A 2025 optical-lattice study up to $24 \\times 24$ sites reported the random-disorder crossover drifting to higher W with system size, consistent with avalanches (identifier not verified).",
          "how": [
            "outside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mit-2d-electrons.mass-divergence",
      "fields": {
        "precise": {
          "text": "In low-disorder (100) Si-MOSFETs ($n_{\\mathrm{c}} \\sim 10^{11}\\ \\mathrm{cm}^{-2}$) and Si/SiGe quantum wells, determine whether m*(n), obtained from thermodynamic magnetization (d mu/d B) and from quantum oscillations, diverges as m*/m_b ~ (n - $n_m$)^(-alpha) at a finite density n_m; whether n_m equals $n_{\\mathrm{c}}$ within error; and whether the spin susceptibility g* m* diverges at the same density (flat-band versus Stoner-type instability).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mit-2d-electrons.metallic-origin",
      "fields": {
        "settled_by": {
          "text": "A quantitative fit of $\\rho(T, n, B_{\\mathrm{parallel}})$ in several materials, with impurity density and Fermi-liquid parameters fixed by independent measurements, that excludes the competing mechanisms.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.mit-2d-electrons.parallel-field-suppression",
      "fields": {
        "precise": {
          "text": "In Si-MOSFETs near $n_c$ an in-plane field $B_{\\mathrm{parallel}}$ raises $\\rho$ by one to two orders of magnitude and saturates at $B_c(n)$, where the electrons become fully spin polarized; above $B_c$ the metallic $\\mathrm{d}\\rho/\\mathrm{d}T > 0$ is lost in Si-MOSFETs, while in ultra-clean SiGe/Si/SiGe wells a metallic state and a metal-insulator transition survive in the fully polarized (spinless, two-valley) system (Melnikov et al. 2020). Explain the magnitude of the positive magnetoresistance and its saturation at $B_c$, explain why the spinless two-valley system stays metallic while the Si-MOSFET does not, and give the ratio $n_c(B > B_c)/n_c(0)$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-graphene-superconductivity.insulator-sc-relation",
      "fields": {
        "title": {
          "text": "Does magic-angle superconductivity require the neighbouring correlated insulator?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-graphene-superconductivity.isotope-effect",
      "fields": {
        "precise": {
          "text": "For magic-angle devices built from 13C-enriched graphene, measure the isotope coefficient $\\alpha_{\\mathrm{iso}} = -d \\ln T_c / d \\ln M$ at fixed twist angle, filling and heterostrain, and compare it with the value each candidate mechanism predicts. For pairing by K-point optical phonons ($\\hbar \\omega \\sim 0.15\\,\\mathrm{eV}$ $>> \\text{ flat-band width}$ $W \\sim 10\\,\\mathrm{meV}$) the anti-adiabatic regime can give $\\alpha_{\\mathrm{iso}}$ well below the BCS value 0.5; a purely electronic mechanism gives $\\alpha_{\\mathrm{iso}} \\sim 0$. Since $\\ln(13/12) = 0.08$, the answer is $\\alpha_{\\mathrm{iso}}$ with an error bar small enough to separate the computed predictions, which requires a statistical ensemble of devices.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-graphene-superconductivity.pairing-mechanism",
      "fields": {
        "title": {
          "text": "What binds electron pairs in magic-angle graphene superconductors?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-tmd-hubbard.continuous-mott",
      "fields": {
        "plain": {
          "text": "In $\\mathrm{MoTe_2}$/$\\mathrm{WSe_2}$ and in twisted $\\mathrm{WSe_2}$, the insulator with one electron per moire site turns into a metal as an electric field widens the band, and the change looks continuous, which standard theory does not expect for this kind of transition.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{MoTe_2}$/$\\mathrm{WSe_2}$ heterobilayers (Li et al., Nature, 2021, arXiv:2103.09779) and twisted bilayer $\\mathrm{WSe_2}$ (Ghiotto et al., Nature, 2021) at filling $\\nu = 1$ (one hole per moire site of a triangular lattice), tuning the displacement field drives a metal-insulator transition at which the charge gap closes continuously and $\\rho(T)$ shows quantum-critical scaling. Determine whether this is a continuous Mott transition from a Fermi liquid to a spin liquid with a spinon Fermi surface, a transition into a magnetically ordered insulator, or a disorder-broadened first-order transition. An answer specifies the insulating state, the critical exponents, and the behaviour of the effective mass and spin susceptibility at the critical point.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-tmd-hubbard.kondo-breakdown",
      "fields": {
        "plain": {
          "text": "In $\\mathrm{MoTe_2}$/$\\mathrm{WSe_2}$ one layer can hold fixed local magnetic moments while the other carries mobile electrons, and the two combine into a heavy-electron metal (a Kondo lattice); how this metal breaks apart when the coupling between layers is weakened is unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{MoTe_2}$/$\\mathrm{WSe_2}$ heterobilayers with the $\\mathrm{MoTe_2}$ moire band at filling $\\nu_f = 1$ (local moments) and the $\\mathrm{WSe_2}$ band doped to density $n_c$ per moire cell, Zhao et al. (Nature, 2023, arXiv:2211.00263) reported a heavy Fermi liquid with a large Fermi surface and gate-tunable Kondo temperature, destroyed by magnetic field. Determine whether reducing the Kondo coupling by displacement field or field produces a Kondo-breakdown transition at which the Fermi-surface volume jumps from $\\nu_f + n_c$ to $n_c$ per moire cell, whether it is continuous, and whether it coincides with magnetic order of the moments. An answer is the Hall number and quasiparticle mass across the transition at $T \\to 0$ and the magnetic state on each side.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.moire-tmd-hubbard.wigner-crystal-melting",
      "fields": {
        "plain": {
          "text": "At fractional fillings such as one electron per three moire sites, electrons in $\\mathrm{WSe_2}$/$\\mathrm{WS_2}$ order into crystals because of their repulsion (generalized Wigner crystals), and how these crystals turn into metals as the repulsion is weakened is unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{WSe_2}$/$\\mathrm{WS_2}$ and similar heterobilayers, insulating states at fractional fillings $\\nu = 1/3, 1/2, 2/3$ and others were detected optically (Regan et al., Nature, 2020, arXiv:1910.09047) and later imaged. As the ratio of Coulomb energy to bandwidth, or the screening length set by gate distance, is reduced, determine whether each crystal melts into a Fermi liquid directly (first or second order) or through intermediate phases such as stripes, bubbles, microemulsions or a quantum-melted state without charge order but with insulating transport. An answer is a phase diagram versus $\\nu$ and screening length with the order of each transition.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.multiferroics.monolayer-type-ii",
      "fields": {
        "title": {
          "text": "Direct electrical measurement of polarization in monolayer $\\mathrm{NiI_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Type-II multiferroics are materials whose spiral spin order itself creates electric polarization. A single atomic layer of $\\mathrm{NiI_2}$ has been shown to host the spin spiral, but its electric polarization has not been measured directly.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Single-layer $\\mathrm{NiI_2}$ shows a canted spin spiral with charge modulation in spin-polarized STM. Measure the spin-induced polarization $P$ and its onset temperature $T_{c}$ directly, by electrical (pyroelectric or switching current) or piezoresponse probes, and test whether $P$ reverses with the spiral chirality. An answer is the measured $P(T)$ and $T_{c}$ with the chirality dependence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.multiferroics.room-temperature-strong-coupling",
      "fields": {
        "plain": {
          "text": "$\\mathrm{BiFeO_3}$ is magnetic and ferroelectric at room temperature but has almost no net magnetization, while materials with strong coupling between the two orders work only at low temperature. No single material yet combines both at room temperature.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Identify a single-phase compound with ferroelectric polarization above about $3 \\times 10^{3}\\ \\mathrm{statC}/\\mathrm{cm}^{2}$ and net magnetization above $10\\ \\mathrm{emu}/\\mathrm{cm}^{3}$ at $T = 300\\ \\mathrm{K}$, in which an electric field deterministically reverses (or rotates by $90\\ \\text{degrees}$) the magnetization. An answer is a material with measured $P$, $M$ and demonstrated electric-field reversal of $M$ at $300\\ \\mathrm{K}$ without a ferromagnetic overlayer.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Deterministic switching at $300\\,\\mathrm{K}$ so far uses $\\mathrm{BiFeO_3}$ coupled to a ferromagnetic layer (Heron et al., Nature 2014).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.multiferroics.switching-energy-bound",
      "fields": {
        "precise": {
          "text": "For a single-domain magnetoelectric element of volume $V$ that must remain thermally stable (anisotropy energy $K_u V \\ge 40 k_B T$ at $T = 300\\,\\mathrm{K}$), derive a lower bound $W_{\\min}$ on the energy supplied by the electric field to reverse the magnetization deterministically, in terms of the spontaneous polarization $P_s$, coercive field $E_c$, magnetoelectric coupling and $V$, and determine whether $W_{\\min}$ can lie below about $10^{-11}\\,\\mathrm{erg}$ with a bias below about $3 \\times 10^{-4}\\,\\mathrm{statvolt}$. An answer is the bound with its derivation and the material parameters that reach it.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "A target of about $10^{-11}$ erg per bit at about $3 \\times 10^{-4}$ statvolt was set for magnetoelectric spin-orbit logic (Manipatruni et al., Nature 2019).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nickelates.ambient-density-wave",
      "fields": {
        "title": {
          "text": "Nature of the density-wave order in ambient-pressure $\\mathrm{La_3Ni_2O_7}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "At normal pressure $\\mathrm{La_3Ni_2O_7}$ does not superconduct but forms a density wave, a periodic pattern of spins and possibly charges, near $150\\ \\mathrm{K}$; its form and its link to superconductivity are uncertain.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "precise": {
          "text": "Identify the spin and charge density-wave order of $\\mathrm{La_3Ni_2O_7}$ at ambient pressure (onset near $150\\ \\mathrm{K}$): wavevector, moment size and arrangement on the bilayer, and any charge component. Determine whether suppression of this order under pressure or strain is necessary for superconductivity. An answer is a refined magnetic structure from neutron or resonant x-ray scattering plus a phase diagram showing where the order vanishes relative to the superconducting onset.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nickelates.bilayer-pairing-symmetry",
      "fields": {
        "title": {
          "text": "Gap symmetry and pairing mechanism of bilayer $\\mathrm{La_3Ni_2O_7}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "In $\\mathrm{La_3Ni_2O_7}$ electrons in two nickel orbitals take part, and it is unknown whether pairs form mainly between the two layers of each bilayer or within each layer as in cuprates.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For bilayer $\\mathrm{La_3Ni_2O_7}$ (hydrostatic pressure above $\\sim 140\\,\\mathrm{kbar}$, or compressively strained films), determine the gap symmetry (interlayer $s\\pm$ between bonding and antibonding d_z2-derived bands, or d-wave dominated by d_x2-y2) and the dominant pairing interaction (interlayer superexchange of d_z2 orbitals, Hund-coupled spin fluctuations). An answer is a momentum-resolved or phase-sensitive gap measurement plus a model reproducing $T_c \\sim 80\\,\\mathrm{K}$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nickelates.bulk-sc-polymorph",
      "fields": {
        "title": {
          "text": "Which $\\mathrm{La_3Ni_2O_7}$ polymorph carries bulk superconductivity under pressure?",
          "how": [
            "outside:chemical",
            "title:owner"
          ]
        },
        "plain": {
          "text": "Early pressure experiments found only a small superconducting volume, and $\\mathrm{La_3Ni_2O_7}$ crystals contain two stacking patterns of nickel-oxide layers, so which structure superconducts in bulk was unclear.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine which structural polymorph of $\\mathrm{La_3Ni_2O_7}$ at high pressure (bilayer 2222 or alternating monolayer-trilayer 1313) carries the $\\sim 80\\,\\mathrm{K}$ superconductivity, and whether the superconducting volume fraction in phase-pure stoichiometric crystals is bulk. An answer combines diffraction under pressure with ac susceptibility volume fractions on the same phase-pure samples.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Bulk superconductivity was reported in $\\mathrm{La_2PrNi_2O_7}$ under pressure (2024) and in pressurized bilayer nickelate crystals up to about $96\\,\\mathrm{K}$ (2025), and superconductivity was also reported in the 1313 polymorph (2025).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nickelates.infinite-layer-films-only",
      "fields": {
        "status_note": {
          "text": "Samarium-based infinite-layer films reached about $40\\ \\mathrm{K}$ (2025); a 2026 preprint reports low-volume-fraction, non-percolative superconductivity at ambient pressure in bulk crystals of the related square-planar trilayer nickelates (La,Pr)4Ni3O8 and (La,Y)4Ni3O8, so bulk superconductivity with full shielding is not established.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nickelates.strain-tc-ceiling",
      "fields": {
        "title": {
          "text": "How high can $T_{c}$ reach in ambient-pressure nickelate films?",
          "how": [
            "title:owner"
          ]
        },
        "status_note": {
          "text": "Onset $T_{c}$ rose from about $40\\ \\mathrm{K}$ (early 2025) to about $63\\ \\mathrm{K}$, with zero resistance near $37\\ \\mathrm{K}$, in (La,Pr)3Ni2O7 films on $\\mathrm{SrLaAlO_4}$ (reported late 2025, published 2026).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.non-abelian-quantum-hall.edge-equilibration",
      "fields": {
        "title": {
          "text": "Does partial edge equilibration explain the $5/2$ thermal Hall value?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.non-abelian-quantum-hall.fibonacci-twelve-fifths",
      "fields": {
        "title": {
          "text": "Is the $12/5$ quantum Hall state a Fibonacci anyon phase?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.non-abelian-quantum-hall.five-halves-order",
      "fields": {
        "title": {
          "text": "Which topological order describes the $5/2$ quantum Hall state?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.nonthermal-fixed-points.quantum-beyond-classical",
      "fields": {
        "title": {
          "text": "Do quantum fluctuations change nonthermal fixed-point exponents?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.one-over-f-noise.dutta-horn-test",
      "fields": {
        "precise": {
          "text": "In the Dutta-Horn model $S(f, T)$ is a superposition of Lorentzians from thermally activated fluctuators with rates $\\left(1/\\tau_0\\right) \\exp(-E/T)$ and a smooth activation-energy distribution $D(E)$; it predicts $\\alpha(f, T) = 1 - (d \\ln S/d \\ln T - 1)/\\ln(2 \\pi f \\tau_0)$, where $\\alpha = -d \\ln S/d \\ln f$. For thin metal films (for example Au, Cu, Ag, Bi) over $f \\sim 10^{-3} \\text{ to } 10^{3}\\,\\mathrm{Hz}$ and $T \\sim 10 \\text{ to } 500\\,\\mathrm{K}$, determine whether this relation holds with a single $\\tau_0$, and whether $D(E)$ inferred from the noise matches $D(E)$ obtained independently (from internal friction or defect spectroscopy).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.one-over-f-noise.flux-noise-spins",
      "fields": {
        "precise": {
          "text": "Low-frequency flux noise $S_{\\Phi}(1\\,\\mathrm{Hz})^{1/2} \\sim 1-10\\,\\mathrm{micro}-\\Phi_0/\\mathrm{Hz}^{1/2}$ ($\\Phi_0=hc/2e$), weakly dependent on loop area, is attributed to surface spins of density $\\sim 5 \\times 10^{13}\\,\\mathrm{cm}^{-2}$ (Koch, DiVincenzo and Clarke 2007). Identify the spin species (adsorbed $\\mathrm{O_2}$, hydrogen, dangling bonds) and the dynamics producing $1/f$ (spin clusters, spin-glass dynamics, spin diffusion), consistent with the measured temperature dependence and the correlation between flux noise and inductance noise.",
          "how": [
            "inside:e-notation",
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.one-over-f-noise.hooge-parameter",
      "fields": {
        "precise": {
          "text": "In $S_R(f)/R^{2} = \\alpha_H/(N_c f)$, measured $\\alpha_H$ spans more than four orders of magnitude between high-quality crystals and disordered films, around the originally proposed universal value $2 \\times 10^{-3}$. For one material class (for example metal films or doped Si), determine how $\\alpha_H$ depends on the density and type of mobile defects, whether the noise arises from mobility or carrier-number fluctuations, and derive $\\alpha_H$ from a microscopic fluctuator model with independently measured defect parameters.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.one-over-f-noise.low-frequency-cutoff",
      "fields": {
        "precise": {
          "text": "The integral of a $1/f$ spectrum diverges logarithmically at both ends, so a physical system needs a lower cutoff $f_{\\min}$, set in the fluctuator picture by the longest relaxation time $\\tau_{\\max} \\sim \\tau_0 \\exp(E_{\\max}/T)$. Measurements over many decades have not found a flattening. Determine $f_{\\min}$ in a specific well-characterized system (metal film or SQUID) and relate it to the fluctuator distribution.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.phonon-thermal-hall.cuprate-chiral-phonons",
      "fields": {
        "precise": {
          "text": "In hole-doped cuprates inside the pseudogap phase and in the Mott insulators $\\mathrm{La_2CuO_4}$ and $\\mathrm{Sr_2CuO_2Cl_2}$, a large negative $\\kappa_{xy}$, present for heat flow both in the $\\mathrm{CuO_2}$ planes and along $c$, is attributed to phonons (Grissonnanche et al. 2019, 2020); a planar thermal Hall response with $B$ in the plane was reported in 2024 (Chen et al., Physical Review X 14, 041011). Identify what couples phonons to $B$ (spin fluctuations of the antiferromagnetic background, defects, or charge-order domains) and predict the doping, field-direction and temperature dependence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.phonon-thermal-hall.intrinsic-or-defect",
      "fields": {
        "title": {
          "text": "Intrinsic versus defect-driven phonon thermal Hall effect in $\\mathrm{SrTiO_3}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "The effect could come from the phonons themselves or from the way they scatter off impurities. $\\mathrm{SrTiO_3}$, where it is large, is a clean place to decide.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{SrTiO_3}$ with $\\kappa_{xy}/\\kappa_{xx}$ up to $\\sim 3 \\times 10^{-3}$ at $9 \\times 10^{4}\\,\\mathrm{G}$ near the $\\kappa_{xx}$ maximum, determine whether $\\kappa_{xy}$ arises from band-intrinsic phonon chirality (for example involving the soft polar mode and structural domains) or from extrinsic skew scattering, by establishing how $\\kappa_{xy}$ scales with $\\kappa_{xx}$ and with controlled defect density (oxygen vacancies, isotope substitution).",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "$\\kappa_{xy}$ measured on crystals with independently quantified defect density, combined with first-principles phonon Berry curvature for $\\mathrm{SrTiO_3}$.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "In $\\mathrm{SrTiO_3}$ disorder and strain suppress $\\kappa_{xy}$ and annealing partly restores it without changing $\\kappa_{xx}$ (Xiang et al., npj Quantum Materials 11, 40, 2026, arXiv 2511.08932); the authors read this as an intrinsic lattice effect sensitive to imperfections, not yet tied to a microscopic mechanism.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.phonon-thermal-hall.nonmagnetic-coupling",
      "fields": {
        "precise": {
          "text": "Crystalline quartz shows a phonon thermal Hall signal, larger in cleaner crystals, while amorphous $\\mathrm{SiO_2}$ does not (Ling, Fauque and Behnia, SciPost Physics 21, 036, 2026), and estimates based on the Lorentz force on ionic Born charges have not been shown to account for the magnitude. Derive the magnitude of $\\kappa_{xy}$ in a diamagnetic crystal from a microscopic coupling (Born effective charges, molecular Berry phases, or the lattice Aharonov-Bohm phase of Behnia, SciPost Physics Core 8, 061, 2025) and explain its absence in the glass.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.phonon-thermal-hall.ubiquity-mechanism",
      "fields": {
        "precise": {
          "text": "In insulators including $\\mathrm{SrTiO_3}$, cuprate parent compounds, Kitaev candidates, garnets, quartz, MgO and intrinsic Si and Ge, fields of tens of kG produce a thermal Hall conductivity $\\kappa_{xy}$ carried by phonons, with thermal Hall angle $\\kappa_{xy}/\\kappa_{xx}$ up to $\\sim 3 \\times 10^{-3}\\text{ at }9 \\times 10^{4}\\,\\mathrm{G}$, typically peaking near the maximum of $\\kappa_{xx}$. Identify the coupling: intrinsic Berry curvature of phonon bands from spin-lattice or ionic Lorentz-type coupling, skew scattering off charged or magnetic defects, or resonant scattering by dynamical defects. An answer predicts magnitude, sign and temperature dependence across materials.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Phonon thermal Hall signals with a common scaling $\\kappa_{xy} \\sim \\kappa_{xx}^2$ were reported in many nonmagnetic crystals ($\\mathrm{SrTiO_3}$, quartz, MgO, $\\mathrm{MgAl_2O_4}$, Si, Ge; Jin et al., arXiv 2404.02863, 2024); no coupling mechanism accounts for magnitude and sign across materials.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.quantum-spin-glasses.glass-phase-bottlenecks",
      "fields": {
        "precise": {
          "text": "For the transverse-field Edwards-Anderson model in $d = 2\\ \\text{and}\\ 3$, and its infinite-range (Sherrington-Kirkpatrick) limit, at $0 < \\Gamma < \\Gamma_c$, determine the probability that the instantaneous ground state has an avoided crossing as $\\Gamma$ decreases to 0, and the scaling of the minimum gap $\\Delta_{\\min}$ with N: $\\exp(-c N^a)$ with the value of a, or a power law. An answer gives the typical $\\Delta_{\\min}(N)$ and its distribution over disorder samples.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.quantum-spin-glasses.lihoyf-glass-phase",
      "fields": {
        "plain": {
          "text": "$\\mathrm{LiHoYF_4}$ is a crystal in which magnetic holmium ions are diluted by nonmagnetic yttrium, and a sideways field adds quantum fluctuations. Experiments disagree on whether its low-temperature state is a genuine spin glass, so it is unclear whether it realizes a quantum spin-glass transition.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.qubit-decoherence-defects.excess-quasiparticles",
      "fields": {
        "precise": {
          "text": "In Al-based qubits at $T \\sim 20\\,\\mathrm{mK}$, the thermal quasiparticle fraction $x_{qp} \\sim \\sqrt{2 \\pi T/\\Delta}\\,\\exp(-\\Delta/T)$ is below $10^{-40}$, while measured $x_{qp}$ ranges from $\\sim 10^{-11}$ to $10^{-5}$. Known sources are stray infrared photons, ionizing radiation (gamma rays, cosmic-ray muons) and phonon bursts from stress relaxation (Mannila et al. 2022). With infrared shielding, radiation shielding and gap engineering in place, determine the residual $x_{qp}$ and charge-parity switching rate and identify the remaining generation mechanism.",
          "how": [
            "inside:e-notation",
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "With multilayer infrared shielding the parity-switching rate fell by four orders of magnitude to $0.069\\ \\mathrm{Hz}$, an inferred $x_{\\mathrm{qp}} \\sim 1.9 \\times 10^{-11}$ (Lin et al., arXiv 2606.07339, 2026); the residual source in shielded devices is unidentified.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.qubit-decoherence-defects.junction-tls-identity",
      "fields": {
        "status_note": {
          "text": "A 2026 ab initio study proposes hydrogen tunneling in $\\mathrm{Nb_2O_5}$ and $\\mathrm{Ta_2O_5}$ as the defects (Mendez and Arias, arXiv 2603.17194); experimental confirmation is lacking.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.qubit-decoherence-defects.resonator-loss-power-law",
      "fields": {
        "settled_by": {
          "text": "$\\tan\\delta$ measured over many decades of photon number and temperature on resonators whose defect density and spectral-diffusion rates are measured independently (for example by two-tone spectroscopy), compared with the interacting-defect prediction without free parameters.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.rhombohedral-graphene.chiral-superconductor",
      "fields": {
        "title": {
          "text": "Is rhombohedral graphene a chiral topological superconductor?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Han et al. (Nature 643, 654, 2025) found two superconducting states with $T_c$ up to 300 mK at $n$ down to $2.4 \\times 10^{11}\\,\\mathrm{cm}^{-2}$ in rhombohedral tetralayer and pentalayer graphene without moire, emerging from a spin- and valley-polarized quarter metal and showing anomalous-Hall hysteresis. Determine the pairing symmetry and whether the state is topological, i.e., its Bogoliubov Chern number and number of chiral Majorana edge modes. An answer gives both with direct evidence.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.rhombohedral-graphene.fqah-quantization",
      "fields": {
        "precise": {
          "text": "In rhombohedral multilayer graphene/hBN at $B=0$, determine whether the FQAH states at $\\nu=2/3,\\ 3/5$ and others reach $R_{xy}=h/(\\nu e^{2})$ within $10^{-3}$ with $R_{xx}\\to0$ as $T\\to0$, and extract their activation gaps. Early (2024) data had $R_{xx}$ of order kilo-ohms. An answer gives quantization accuracy and gap for each state.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.rhombohedral-graphene.moire-role",
      "fields": {
        "title": {
          "text": "Is the moire potential needed for fractional anomalous Hall states?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.rhombohedral-graphene.repulsive-pairing",
      "fields": {
        "precise": {
          "text": "For a spin- and valley-polarized rhombohedral graphene band at $n \\sim 10^{11}-10^{12}\\,\\mathrm{cm}^{-2}$ with gate-screened Coulomb interaction, compute the odd-parity pairing $T_c$ from Kohn-Luttinger, Berry-curvature-enhanced or order-parameter-fluctuation mechanisms and compare with phonon-mediated odd-parity pairing. An answer is a calculation reproducing $T_c \\sim 0.1-0.3\\,\\mathrm{K}$ and its density and displacement-field window.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.rhombohedral-graphene.trilayer-bilayer-pairing",
      "fields": {
        "precise": {
          "text": "Rhombohedral trilayer graphene superconducts with $T_{c}$ up to about 100 mK next to isospin-symmetry-breaking transitions (Zhou et al., Nature, 2021, doi:10.1038/s41586-021-03926-0), and Bernal bilayer graphene superconducts under in-plane magnetic field or with spin-orbit coupling induced by an adjacent $\\mathrm{WSe_2}$ layer. Determine whether pairing is mediated by acoustic phonons (Chou et al., PRL 127, 187001, 2021) or by isospin fluctuations or Kohn-Luttinger repulsion (e.g., Chatterjee et al., Nature Communications, 2022, doi:10.1038/s41467-022-33561-w). An answer reproduces $T_{c}(n,D)$ in both systems and predicts the response to gate screening.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.scars-fragmentation.pxp-thermodynamic-limit",
      "fields": {
        "title": {
          "text": "Do PXP scar eigenstates survive as the chain becomes infinite?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.scars-fragmentation.tilted-hubbard-relaxation",
      "fields": {
        "precise": {
          "text": "In a Fermi-Hubbard chain with tunneling $J$, interaction $U$ and potential step $\\Delta$ per site ($\\Delta >> J, U$, away from resonances $\\Delta = n U$), the order-$J^2/\\Delta$ effective Hamiltonian conserves dipole moment and is fragmented. Higher-order terms keep dipole conservation (valid up to times exponential in $\\Delta/\\max(J,U)$) but connect fragments. Determine the decay time $\\tau$ of a density-wave imbalance as a function of $\\Delta/J$ and $U/J$ as $L \\to \\infty$, set by these fragment-connecting processes; answer: the scaling form of $\\tau$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sign-problem-numerics.analytic-continuation-limits",
      "fields": {
        "precise": {
          "text": "Given $G(\\tau) = \\int \\mathrm{d}w\\, K(\\tau, w) A(w)$ with $K = \\exp(-\\tau w)/(1 + \\exp(-\\beta w))$ on $0 \\le \\tau \\le \\beta$ and Gaussian noise of size $\\sigma$, determine the optimal resolution of the spectral function $A(w)$ (minimal resolvable width and amplitude of a feature at frequency $w$) as a function of $\\sigma, \\beta \\text{ and } w$, and construct estimators (maximum entropy, stochastic, Nevanlinna, Bayesian) with certified error bounds that reach it. An answer is proven bounds plus an estimator attaining them on benchmarks.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sign-problem-numerics.certified-2d-bounds",
      "fields": {
        "precise": {
          "text": "At $U/t = 8$ and filling $n = 0.875$ with $t' = 0$, DMRG, constrained-path auxiliary-field Monte Carlo, infinite projected entangled-pair states and density-matrix embedding agree on $E/N$ to about $0.01\\,t$, while candidate stripe and uniform d-wave states differ by energies of order $10^{-3}\\,t$ (Zheng et al., Science 2017). Construct methods giving rigorous lower bounds (e.g. reduced-density-matrix semidefinite programs) and variational upper bounds for $E/N$ and for long-distance pair correlations in the thermodynamic limit, with gap below $10^{-3}\\,t$. An answer is a certified interval and the scaling of its width with computational cost.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "A computation producing upper and lower bounds on E/N for the infinite lattice separated by less than $10^{-3}$ t, together with bounds on pair correlations.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sign-problem-numerics.dynamical-sign-problem",
      "fields": {
        "precise": {
          "text": "Real-time diagrammatic and path-integral Monte Carlo for nonequilibrium Green's functions have variance growing as $\\exp(c t)$. Inchworm Monte Carlo (Cohen et al. 2015) and related methods reach polynomial scaling in t for Anderson impurity models. Determine whether a classical algorithm computes local real-time correlators of the infinite 2D Hubbard model at $U/t \\sim 4$, starting from a thermal state at $T \\sim t$, up to time $t_{\\max}$ with error $\\epsilon$ at cost polynomial in $t_{\\mathrm{max}}$ and $1/\\epsilon$, or prove that this is hard (e.g. by a complexity reduction). An answer is an algorithm with proven scaling or a hardness proof.",
          "how": [
            "inside:operator-word",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sign-problem-numerics.intrinsic-sign-problem",
      "fields": {
        "title": {
          "text": "Which phases of matter carry an intrinsic sign problem?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sit-anomalous-metal.cooper-pair-insulator",
      "fields": {
        "precise": {
          "text": "In amorphous InOx, TiN and nanopatterned Bi films on the insulating side of the field-tuned transition, $\\rho \\sim \\exp(T_{0}/T)$ with $T_{0}$ peaking at a field $B_{\\mathrm{peak}}$, the magnetoresistance peak spans several orders of magnitude, and patterned films show $h/2e$ periodic magnetoresistance (Stewart et al. 2007). Explain the pair-localization mechanism and $T_{0}(B)$, and determine whether abrupt current jumps in the $I-V$ curves reflect electron overheating (Altshuler, Kravtsov, Lerner and Aleiner 2009) or a distinct phase (proposed superinsulator).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sit-anomalous-metal.intrinsic-saturation",
      "fields": {
        "precise": {
          "text": "In $2\\mathrm{D}$ superconducting films and arrays (amorphous InOx, MoGe, Ta, transition-metal dichalcogenide superconductors, Josephson-junction arrays) tuned by $B$, gate or disorder near the superconductor-insulator transition, $\\rho(T)$ saturates below $T \\sim 0.1\\,T_c$ at $10^{-3}\\ \\text{to}\\ 10^{-1}$ of the normal-state value. Determine whether the saturation survives when electron temperature and external radiation are independently controlled (filtered leads, shielding, noise thermometry), i.e. whether $\\rho(T \\to 0) > 0$ holds in a finite parameter range.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.skyrmion-magnets.centrosymmetric-mechanism",
      "fields": {
        "title": {
          "text": "What stabilizes skyrmion lattices in centrosymmetric magnets like $\\mathrm{Gd_2PdSi_3}$?",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Most skyrmions appear in crystals lacking mirror symmetry, where a twisting interaction favors them. $\\mathrm{Gd_2PdSi_3}$ and $\\mathrm{GdRu_2Si_2}$ have that symmetry yet host very small skyrmions, and the competing explanations involve geometric frustration or interactions carried by conduction electrons.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "For $\\mathrm{Gd_2PdSi_3}$ (triangular) and $\\mathrm{GdRu_2Si_2}$ (tetragonal), with skyrmion-lattice periods of about 2 to 3 nm, determine which mechanism stabilizes the multi-$q$ state: frustrated RKKY couplings, Fermi-surface-driven biquadratic and four-spin interactions, or dipolar and anisotropy effects. An answer is a microscopic model derived from the measured band structure that reproduces the field-temperature phase diagram and the modulation vectors.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.skyrmion-magnets.lattice-melting-2d",
      "fields": {
        "status_note": {
          "text": "Huang et al. (Nature Nanotechnology 2020) observed a hexatic skyrmion phase in thin $\\mathrm{Cu_2OSeO_3}$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.skyrmion-magnets.quantum-skyrmions",
      "fields": {
        "precise": {
          "text": "In a frustrated or chiral magnet with $S=1/2\\ \\text{or}\\ 1$ local moments and skyrmion radius of a few lattice spacings, detect a quantum signature: macroscopic quantum tunneling of skyrmion number or position (a temperature-independent switching rate below a crossover $T*$), or quantized internal modes inconsistent with classical spin dynamics. An answer is an identified system and measurement giving $T*$ and the rate.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Low-temperature single-skyrmion switching or spectroscopy showing a temperature-independent rate below $T*$, compared with quantum many-body calculations.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.skyrmion-magnets.topological-hall-artifacts",
      "fields": {
        "precise": {
          "text": "For films and heterostructures ($\\mathrm{SrRuO_3}$-based, Mn-based, magnetic topological insulators) with reported humps in $\\rho_{xy}(H)$, determine for each whether the hump follows $\\rho_{TH} \\sim P R_0 n_{sk} \\Phi_0$ ($P$ spin polarization, $R_0$ ordinary Hall coefficient, $n_{sk}$ skyrmion density, $\\Phi_0$ flux quantum) or arises from superposed anomalous Hall loops of opposite sign. An answer is a criterion that separates the two and its application with direct imaging of $n_{sk}$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.spin-ice.dy2ti2o7-ground-state",
      "fields": {
        "title": {
          "text": "Does classical spin ice $\\mathrm{Dy_2Ti_2O_7}$ order or keep its Pauling entropy?",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{Dy_2Ti_2O_7}$, determine whether thermal equilibrium below 0.5 K approaches the ordered state predicted by the dipolar spin-ice model (transition near 0.18 K) with loss of the Pauling entropy $(R/2)\\ln(3/2)$ per mole Dy, or retains a disordered ice manifold. An answer is the equilibrium entropy and any ordering wavevector as $T \\to 0$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.spin-ice.emergent-photon-evidence",
      "fields": {
        "plain": {
          "text": "Quantum spin ice should host three kinds of emergent particles: photons, electric-like spinons and magnetic monopoles. Cerium pyrochlores such as $\\mathrm{Ce_2Zr_2O_7}$ show signs of these, but alternative explanations are not fully excluded.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{Ce_2Zr_2O_7}$, $\\mathrm{Ce_2Sn_2O_7}$ and $\\mathrm{Ce_2Hf_2O_7}$ (dipolar-octupolar doublets), establish the $\\mathrm{U}(1)$ quantum spin liquid through its distinct signatures: a gapless linearly dispersing transverse photon ($C \\sim T^{3}$ well below the photon bandwidth), a spinon continuum, and their predicted spectral weights. An answer is a fit of thermodynamic and neutron data by quantum spin ice theory with independently fixed exchange parameters that excludes classical or disorder-driven alternatives.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Gao et al. (Nature Physics 2025) reported neutron and thermodynamic evidence for emergent photons and spinons in $\\mathrm{Ce_2Zr_2O_7}$, interpreted as a pi-flux quantum spin ice.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.spin-ice.monopole-noise",
      "fields": {
        "title": {
          "text": "Origin of anomalous magnetic noise from monopoles in $\\mathrm{Dy_2Ti_2O_7}$",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{Dy_2Ti_2O_7}$ at $T$ of about 0.5 to 3 K the magnetization-noise spectrum follows $S(\\omega) \\sim \\omega^{-b}$ with $b$ between 1 and 2, and relaxation is faster than Arrhenius would allow at high $T$ and slower at low $T$. Derive $b(T)$ and the relaxation time $\\tau(T)$ from a microscopic dipolar model with monopole hopping, without free parameters beyond the fitted exchange set. An answer is a model reproducing $S(\\omega, T)$ quantitatively.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.spin-ice.photon-heat-capacity",
      "fields": {
        "precise": {
          "text": "In quantum spin ice the photon speed $c$ is set by the ring-exchange scale $g=12J_{\\mathrm{pm}}^{3}/J_{\\mathrm{zz}}^{2}$ ($c \\sim g$ $a$$/\\hbar$ up to a computed prefactor, a the lattice spacing), and the photon heat capacity per volume is $C/V = (4 \\pi^{2}/15) k_{\\mathrm{B}} (k_{\\mathrm{B}} T/\\hbar c)^{3}$ for two polarizations. Measure $C/T^{3}$ below the photon bandwidth in a candidate material and compare $c$ with the value from independently fitted exchange parameters. An answer is $c$ measured and predicted, with agreement or disagreement within errors.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.spin-ice.pi-flux-classification",
      "fields": {
        "precise": {
          "text": "For $\\mathrm{Ce_2Zr_2O_7}$, $\\mathrm{Ce_2Sn_2O_7}$ and $\\mathrm{Ce_2Hf_2O_7}$ described by the dipolar-octupolar Hamiltonian H = sum_<ij> [J_x tau^x_i tau^x_j + J_y tau^y_i tau^y_j + J_z tau^z_i tau^z_j + J_xz (tau^x_i tau^z_j + tau^z_i tau^x_j)], determine the exchange parameters and the sign of the dominant transverse coupling that fixes the zero-flux or $\\pi$-flux $U(1)$ phase, and confirm it by the predicted spinon-continuum structure. An answer is the classification per compound with fitted parameters.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Gao et al. (2025) classify $\\mathrm{Ce_2Zr_2O_7}$ as $\\pi$-flux; parameter fits differ across groups and compounds.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sr2ruo4.gap-nodes",
      "fields": {
        "title": {
          "text": "Location of gap nodes on the $\\mathrm{Sr_2RuO_4}$ Fermi sheets",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In $\\mathrm{Sr_2RuO_4}$, determine whether the gap features along the zone diagonals [110] on the $\\alpha$ and $\\beta$ sheets are symmetry-required vertical line nodes or deep accidental minima, and determine the gap structure on the $\\gamma$ sheet. An answer is momentum-resolved gap data at $T << T_c$ (ARPES with sub-0.1 meV resolution, quasiparticle interference, or field-angle-resolved specific heat) on all three sheets, resolving node versus minimum.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sr2ruo4.order-parameter",
      "fields": {
        "title": {
          "text": "What is the superconducting order parameter of $\\mathrm{Sr_2RuO_4}$?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "The pairing pattern of $\\mathrm{Sr_2RuO_4}$ must explain conflicting data: some measurements suggest a two-part order that breaks time-reversal symmetry, while others see only one transition.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine the order parameter of $\\mathrm{Sr_2RuO_4}$ ($T_c = 1.5\\,\\mathrm{K}$): parity, spin structure, orbital and band content, and irreducible representation of D4h, consistent with the drop of the 17O Knight shift for in-plane fields (2019), the ultrasound jump in shear modulus $c66$ suggesting two components, muSR and polar Kerr time-reversal breaking, and no second heat-capacity anomaly under uniaxial stress. Candidates include d_xz + i d_yz, s' + i d_x2-y2, d + i g and interorbital pairing states.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sr2ruo4.trsb-bulk",
      "fields": {
        "title": {
          "text": "Is time-reversal breaking in $\\mathrm{Sr_2RuO_4}$ an intrinsic bulk property?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "plain": {
          "text": "Muon and optical experiments see signs that the superconducting state of $\\mathrm{Sr_2RuO_4}$ picks a sense of rotation, breaking time-reversal symmetry, but the signal may come from defects.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Determine whether the time-reversal symmetry breaking seen by zero-field muSR and polar Kerr rotation below $T_c$ in $\\mathrm{Sr_2RuO_4}$ is a bulk property of the superconducting order parameter or is tied to dislocations and local strain. An answer compares muSR and Kerr signal size across samples with measured defect density, and tests whether the signal onset follows $T_c$ under stress and disorder.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.sr2ruo4.two-component",
      "fields": {
        "title": {
          "text": "Is the $\\mathrm{Sr_2RuO_4}$ order parameter two-component?",
          "how": [
            "outside:chemical",
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Determine whether uniaxial stress along $[100]$ splits $T_c$ of $\\mathrm{Sr_2RuO_4}$ into two thermodynamic transitions, as a two-component order parameter (multidimensional representation or accidental degeneracy) requires. An answer is a thermodynamic detection of the second transition, or a bound on its specific-heat jump below the value predicted by models fitted to the ultrasound data.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.strange-metals.hall-angle",
      "fields": {
        "precise": {
          "text": "In optimally doped cuprates $\\rho_{xx} \\sim T$ while $\\cot(\\theta_{H}) = \\rho_{xx}/\\rho_{xy} \\sim A + B T^{2}$ over a wide range. Determine whether this requires two distinct relaxation rates (transport and Hall) or follows from a single anisotropic scattering rate on a Fermi surface with hot and cold regions. An answer is a model that reproduces both laws and their doping dependence with one parameter set.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.strange-metals.planckian-universality",
      "fields": {
        "title": {
          "text": "Is the Planckian scattering rate universal, and is it a bound?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.strange-metals.quasiparticle-charge",
      "fields": {
        "title": {
          "text": "Do strange metals carry current in electron-like quasiparticles?",
          "how": [
            "title:question-mark"
          ]
        },
        "status_note": {
          "text": "Strongly suppressed shot noise was reported in $\\mathrm{YbRh_2Si_2}$ nanowires in 2023; whether electron-phonon relaxation can explain it is debated.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.strange-metals.random-yukawa-test",
      "fields": {
        "title": {
          "text": "Does spatially random Yukawa coupling explain strange-metal transport quantitatively?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.strange-metals.t-linear-origin",
      "fields": {
        "precise": {
          "text": "Explain $\\rho(T) = \\rho_0 + A_1 T$ persisting from T well below the Fermi temperature up to and beyond the Mott-Ioffe-Regel limit without saturation, near quantum critical points in cuprates ($p \\sim p*$), $\\mathrm{YbRh_2Si_2}$ and other materials. An answer is a controlled theory of a metal without long-lived quasiparticles in two or three dimensions that yields T-linear resistivity with the measured slope $A_1$ and its doping or field dependence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.syk-holography.experimental-signature",
      "fields": {
        "title": {
          "text": "Has any device shown a measurable SYK-specific signature?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Proposals include irregular graphene flakes in a quantizing magnetic field (Chen et al. 2018) and Majorana-wire arrays. Does any device show a quantity specific to SYK, such as a thermopower set by $\\mathrm{d}S_{0}/\\mathrm{d}Q$, the charge derivative of the residual entropy, or tunneling conductance scaling as $\\max(eV, k_B T)^{-1/2}$? Answer yes or no.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.syk-holography.sparse-syk-threshold",
      "fields": {
        "precise": {
          "text": "In sparse Majorana SYK with $N$ fermions and $k$ $N$ four-body terms chosen at random, find the critical $k_c$ (as $N\\to\\infty$) below which the low-temperature Schwarzian regime and near-maximal Lyapunov exponent are lost, and the $1/k$ corrections above it. Answer: $k_c$, or the scaling of physical quantities with $k$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.syk-holography.wormhole-teleportation",
      "fields": {
        "precise": {
          "text": "The protocol prepares two SYK systems in a thermofield-double state, inserts a qubit, applies a weak coupling of strength $\\mu$, and predicts a teleportation signal peaked near the scrambling time with operator size winding. Jafferis et al. (Nature 2022, doi:10.1038/s41586-022-05424-3) used a learned 7-qubit Hamiltonian; Kobrin, Schuster, Yao (arXiv:2302.07897) argued that it does not thermalize and matches SYK only for the training operators. Determine the minimal N and Hamiltonian class (dense or sparse SYK) for which the signal, its $\\mu$ dependence and size winding are distinguishable from generic small or commuting models. Answer: $N_{\\min}$ with explicit criteria, and whether present hardware reaches it.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.tc-limits.ambient-room-temperature",
      "fields": {
        "title": {
          "text": "Can any material superconduct at room temperature and ambient pressure?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.tc-limits.phonon-tc-bound",
      "fields": {
        "title": {
          "text": "Is there a rigorous upper bound on phonon-mediated $T_{\\mathrm{c}}$?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.tc-limits.stiffness-bound-3d",
      "fields": {
        "title": {
          "text": "Do superfluid-stiffness bounds on $T_c$ extend to three dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.fractional-spin-hall",
      "fields": {
        "title": {
          "text": "Nature of the fractional quantum spin Hall state in twisted $\\mathrm{MoTe_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "At three holes per moire cell, twisted $\\mathrm{MoTe_2}$ near 2.1 degrees conducts along its edges with $3/2$ times the basic conductance quantum $e^{2}/h$ while keeping time-reversal symmetry (no preferred direction of time), and no accepted theory explains it.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Kang et al. (Nature 628, 522, 2024) reported in 2.1 deg twisted bilayer $\\mathrm{MoTe_2}$ at hole filling $\\nu = 3$ a state with vanishing Hall response and edge conductance near $\\left(3/2\\right)e^2/h$, interpreted as a fractional quantum spin Hall state, possibly a time-reversal pair of $3/2$ fractional Chern insulators. Identify its topological order (for example a time-reversal-symmetric non-Abelian state built from two Moore-Read halves, or an Abelian fractional topological insulator) and its edge theory, and determine whether the edge conductance is quantized. An answer is a topological order whose predicted edge conductance, quasiparticle charge and spin response match data.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.one-third-asymmetry",
      "fields": {
        "plain": {
          "text": "In twisted $\\mathrm{MoTe_2}$ the zero-field fractional Hall state at two thirds band filling is clear in transport while the one-third state is fragile or absent, the reverse of the ordinary fractional quantum Hall effect, where one third is the strongest.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In twisted bilayer $\\mathrm{MoTe_2}$ at $\\theta \\sim 3.5-3.9\\,\\mathrm{deg}$, fractional quantum anomalous Hall states are seen in transport at hole fillings $\\nu = -2/3$ and $-3/5$ of the first Chern band (Cai et al., Park et al., Zeng et al., Nature 2023), while at $\\nu = -1/3$ only optical signatures of a fragile state over a narrow displacement-field range have been reported (arXiv:2602.04561). Explain this asymmetry: mixing with the second moire band, Berry-curvature and quantum-metric inhomogeneity, or interaction-induced band renormalization favouring a charge-density wave at $1/3$. An answer is a calculation with independently fixed parameters reproducing the ground state and gap at each filling and its displacement-field range.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.sc-near-fqah",
      "fields": {
        "plain": {
          "text": "Twisted $\\mathrm{MoTe_2}$ superconducts at fillings next to its fractional quantum anomalous Hall states (zero-field fractional Hall states), and it is unknown whether the pairs break time-reversal symmetry and carry topological edge modes.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "A 2025 report (arXiv:2504.06972) found superconductivity in twisted bilayer $\\mathrm{MoTe_2}$ near reentrant integer and fractional quantum anomalous Hall insulators, emerging from a spin- and valley-polarized normal state with anomalous Hall hysteresis. Determine the order parameter (chiral intravalley pairing breaking time reversal versus intervalley pairing) and its Bogoliubov Chern number, i.e., the number of chiral Majorana edge modes. An answer gives the pairing symmetry and edge-mode count with direct evidence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.twse2-superconductivity",
      "fields": {
        "title": {
          "text": "Mechanism of superconductivity in twisted bilayer $\\mathrm{WSe_2}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Twisted $\\mathrm{WSe_2}$ superconducts at twist angles near 3.65 and 5 degrees, next to insulating or possibly magnetic states, and the attraction that pairs its electrons is unknown.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In twisted bilayer $\\mathrm{WSe_2}$ at $\\theta \\sim 3.65\\,\\mathrm{deg}$ and $\\sim 5\\,\\mathrm{deg}$, superconductivity with $T_c$ of a few hundred mK appears near half filling of the top moire band under displacement field, adjacent to a correlated insulator or metal with possible antiferromagnetic order. Determine the pairing interaction (spin fluctuations of a triangular-lattice Hubbard model, valley fluctuations, phonons) and the gap symmetry. An answer reproduces $T_c$ versus displacement field and filling from a microscopic model.",
          "how": [
            "outside:chemical"
          ]
        },
        "status_note": {
          "text": "Reported in 2024-2025 by Cornell (3.65 deg) and Columbia (5.0 deg) groups; a 2026 preprint reports superconductivity in twisted trilayer $\\mathrm{WSe_2}$ (arXiv:2606.11495).",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.zero-field-cfl",
      "fields": {
        "precise": {
          "text": "In twisted bilayer $\\mathrm{MoTe_2}$ at $\\theta \\sim 3.5-3.9\\,\\mathrm{deg}$ near hole filling $\\nu = 1/2$ and $3/4$ of the first Chern band, determine whether the compressible state is an anomalous composite Fermi liquid with Fermi wavevector $k_F = \\sqrt{4 \\pi n_{cf}}$, $n_{cf}$ the composite-fermion density, or an ordinary Fermi liquid with Berry curvature. An answer is a direct measurement of the composite-fermion Fermi surface.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.twisted-tmd.zero-field-nonabelian",
      "fields": {
        "plain": {
          "text": "Some predicted fractional states host non-Abelian anyons, quasiparticles whose exchange changes the system's state in an order-dependent way, and twisted $\\mathrm{MoTe_2}$ may host one with no magnetic field.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Numerics predict Moore-Read-type non-Abelian order at half filling of a higher moire Chern band of twisted $\\mathrm{MoTe_2}$ near $\\theta \\sim 2\\ \\mathrm{deg}$, a band whose wavefunctions resemble the first excited Landau level. Determine whether any zero-field moire Chern band hosts a gapped even-denominator state with non-Abelian order. An answer is a quantized even-denominator $\\sigma_{xy}$ with $R_{xx} \\to 0$ at $B = 0$, plus a half-integer chiral central charge from thermal Hall or $e/4$ quasiparticle charge.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ultrafast-spintronics.angular-momentum-flow",
      "fields": {
        "precise": {
          "text": "In Ni, Co and Fe films pumped at absorbed fluences of order $10^{4}\\,\\mathrm{erg}/\\mathrm{cm}^{2}$, magnetization drops within about 100 to 300 fs (Beaurepaire et al. 1996). Determine the time-resolved partition of the lost spin angular momentum among electron orbital moments, superdiffusive spin currents, magnons and the lattice (circularly polarized phonons, Einstein-de Haas rotation) during 0 to 500 fs, and the microscopic transfer channel (Elliott-Yafet spin-flip scattering, direct spin-phonon coupling). An answer is a quantitative angular-momentum budget versus time.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ultrafast-spintronics.spin-seebeck-origin",
      "fields": {
        "precise": {
          "text": "In YIG/Pt the longitudinal spin Seebeck voltage depends on YIG thickness (saturating over lengths of order $10^{-4}$ cm), magnetic field (suppressed at high field), and temperature, with anomalies where magnons and phonons hybridize (magnon polarons, 2016). Determine the roles of bulk thermal-magnon accumulation, the interfacial magnon-electron temperature difference, and magnon-phonon coupling, and predict the voltage versus thickness, T and field. An answer is one quantitative model reproducing all three dependences.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.ultrafast-spintronics.spin-superfluid-transport",
      "fields": {
        "title": {
          "text": "Has long-distance spin-superfluid transport been demonstrated?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Spin superfluidity predicts a nonlocal spin signal decaying algebraically, $\\sim 1/(L + L_0)$, instead of exponentially, $\\sim \\exp(-L/\\lambda)$, and a critical spin current. Determine whether claimed observations in spin-flop $\\mathrm{Cr_2O_3}$ (Yuan et al. 2018), the graphene quantum Hall antiferromagnet (Stepanov et al. 2018) and magnon condensate supercurrents in YIG (Bozhko et al. 2016) show superfluid spin transport, by measuring the distance dependence and a critical current in a single device free of thermal artifacts. An answer is yes or no.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.weyl-semimetals.axion-cdw",
      "fields": {
        "title": {
          "text": "Is the charge-density wave in (TaSe4)2I an axion insulator?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.weyl-semimetals.chiral-anomaly-magnetoresistance",
      "fields": {
        "title": {
          "text": "Is negative longitudinal magnetoresistance a chiral-anomaly signature?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In Weyl and Dirac semimetals ($\\mathrm{Na_3Bi}$, $\\mathrm{Cd_3As_2}$, the TaAs family, $\\mathrm{ZrTe_5}$), the chiral anomaly predicts a longitudinal conductivity increase $\\Delta \\sigma_{zz} = C_a B^2$ for $E$ parallel to $B$, with $C_a$ proportional to $v^{3}\\tau_v/\\mu^{2}$ ($v$ Fermi velocity, $\\tau_v$ intervalley scattering time, $\\mu$ chemical potential from the node). Determine for each material whether the measured negative magnetoresistance follows this scaling once current jetting and inhomogeneity are excluded. An answer is a material-by-material verdict with $\\tau_v$ measured independently.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.weyl-semimetals.zrte5-hall-plateaus",
      "fields": {
        "title": {
          "text": "Origin of Hall plateaus in bulk $\\mathrm{ZrTe_5}$",
          "how": [
            "outside:chemical"
          ]
        },
        "plain": {
          "text": "Thick crystals of $\\mathrm{ZrTe_5}$ show Hall-resistance plateaus resembling the quantum Hall effect, which normally needs a two-dimensional sample, and whether a field-induced charge-density wave causes them is unsettled.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "In bulk $\\mathrm{ZrTe_5}$ (and $\\mathrm{HfTe_5}$), Tang et al. (Nature, 2019) reported Hall plateaus with $\\rho_{xy}\\sim (1/2)(h/e^2)\\lambda_z$, $\\lambda_z$ the Fermi wavelength along the field, attributed to a field-induced charge-density wave in the quantum limit. Determine whether a density modulation and gap exist or whether the plateau-like features come from quantum-limit band physics alone. An answer is an identification backed by direct structural or spectroscopic evidence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cm.wigner-crystal-2d.intermediate-microemulsion",
      "fields": {
        "precise": {
          "text": "Spivak and Kivelson (2004) argued that a direct first-order transition is forbidden in 2D with $1/r$ interactions, which implies intermediate microemulsion phases (bubbles, stripes) in a window of $r_s$ near $r_s$_c. Determine whether these phases exist in clean 2D jellium and in gated devices where the interaction is screened beyond the gate distance d, their width in $r_s$, and their observable signatures (transport anisotropy, compressibility, local density images).",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cmb-anomalies.chance-or-physics",
      "fields": {
        "precise": {
          "text": "The anomalies are: low quadrupole power, lack of temperature correlation above 60 degrees ($S_1/2$), quadrupole-octopole alignment, hemispherical power asymmetry, the cold spot and an odd-even parity asymmetry, each at $p \\sim 0.1 \\text{ to } 1\\%$ in LCDM, with a posteriori choice of statistics. Decide whether they are flukes or physical by testing predictions fixed in advance on independent data (large-angle E-mode polarization, CMB lensing, galaxy surveys).",
          "how": [
            "inside:percent",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cmb-anomalies.matter-dipole",
      "fields": {
        "precise": {
          "text": "The CMB dipole implies a velocity of about $3.7 \\times 10^{7}\\,\\mathrm{cm/s}$, which predicts a kinematic number-count dipole (Ellis-Baldwin test) for distant sources. CatWISE2020 quasars and NVSS radio galaxies give amplitudes about twice the prediction, reported at about $5\\sigma$ in joint analyses. Determine whether this signals a non-kinematic, intrinsic anisotropy incompatible with FLRW cosmology, or catalog systematics and clustering contributions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cmb-anomalies.polarization-correlation",
      "fields": {
        "precise": {
          "text": "Given the observed temperature map, compute the LCDM conditional distribution of the E-mode statistic $S_1/2^{EE}$ and of the TE correlation at angles above 60 degrees; measure them on a full-sky E-mode map with cosmic-variance-limited noise at multipoles $\\ell < 30$. Answer whether the observed values fall in the tails predicted by a physical suppression or follow LCDM.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cosmic-dawn.lcdm-baryon-limit",
      "fields": {
        "precise": {
          "text": "For a survey volume $V$ at redshift $z$, the most massive LCDM halo $M_h,\\mathrm{max}(z, V)$ bounds the stellar mass by $M_* \\le f_b M_h,\\mathrm{max}$ with $f_b = \\Omega_b / \\Omega_m \\sim 0.16$. Determine whether any galaxy with spectroscopic redshift and stellar mass corrected for active-galactic-nucleus light violates this bound.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cosmic-dawn.population-iii-stars",
      "fields": {
        "precise": {
          "text": "Identify a stellar system with gas metallicity below the critical value $Z_{\\mathrm{crit}}$ (theoretical range about $10^{-6}\\ \\text{to}\\ 1e-3.5\\ Z_{\\mathrm{sun}}$), strong $\\mathrm{He}\\ \\mathrm{II}\\ 1640\\ \\text{Angstrom}$ emission and no detected metal lines, consistent with a top-heavy initial mass function. The leading candidate is LAP1 at $z \\sim 6.6$, lensed by the cluster MACS J0416. An answer is a confirmed detection with metal-line upper limits below $Z_{\\mathrm{crit}}$, or a measured upper bound on the Population III star-formation rate density at $z > 6$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cosmic-magnetism.plasma-instability-cooling",
      "fields": {
        "precise": {
          "text": "For TeV-blazar pair beams with Lorentz factors $\\sim 10^{6}$ traversing void plasma with $n_e \\sim 10^{-7}\\,\\mathrm{cm}^{-3}$ and $T \\sim 10^{4}\\,\\mathrm{K}$, determine whether the nonlinear saturated growth of the electrostatic oblique instability drains beam energy faster than inverse-Compton cooling on the CMB. Answer yes or no from kinetic simulations or analytic theory that includes nonlinear Landau damping and plasma inhomogeneity.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cosmic-magnetism.seed-origin",
      "fields": {
        "precise": {
          "text": "Galaxies and clusters host fields of $\\sim 10^{-6}$ G coherent over $\\sim 10\\,\\mathrm{kpc}$, amplified by dynamos from seeds $B_{\\mathrm{seed}}$. Identify the origin of the seeds: Biermann battery in the first collapsed structures ($\\sim 10^{-20}$ G), inflationary magnetogenesis, or first-order phase transitions. An answer identifies the origin through the void field strength, coherence length and helicity, which differ between scenarios.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.cosmic-magnetism.void-field-strength",
      "fields": {
        "precise": {
          "text": "The absence of GeV cascade emission from TeV blazars gives $B > \\sim 10^{-17} \\text{ to } 10^{-16}\\,\\mathrm{G}$ for coherence lengths $\\lambda_B > \\sim 1\\,\\mathrm{Mpc}$, while CMB and Faraday rotation give upper bounds of order $10^{-9}\\,\\mathrm{G}$. Measure $B$ and $\\lambda_B$ in voids, for example from cascade halos or time-delayed pair echoes. An answer is a measured value, not only a bound.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-energy.cc-problem",
      "fields": {
        "precise": {
          "text": "The observed dark energy density is $\\rho_{\\Lambda} \\sim 6 \\times 10^{-30}\\ \\mathrm{g}/\\mathrm{cm}^{3}$, i.e. $\\rho_{\\Lambda}^{1/4} \\sim 2.3 \\times 10^{-3}\\ \\mathrm{eV}$ in natural units, while Standard Model contributions (electroweak symmetry breaking ~ $(100\\ \\mathrm{GeV})^{4}$, QCD ~ $(0.2\\ \\mathrm{GeV})^{4}$) exceed it by $\\sim 10^{55}$ and $\\sim 10^{44}$, and a Planck-scale cutoff by $\\sim 10^{123}$ (often quoted as $10^{120}$, using the reduced Planck mass). Find a mechanism that yields the observed value without tuning to that precision, or show that environmental selection in a multiverse is the only consistent explanation.",
          "how": [
            "inside:e-notation",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-energy.coincidence-problem",
      "fields": {
        "precise": {
          "text": "With $\\rho_m \\sim a^{-3}$ and a constant $\\rho_\\Lambda$, the ratio $r = \\rho_\\Lambda / \\rho_m = (\\Omega_\\Lambda / \\Omega_m) a^3$ is about 2.2 today and was about $2 \\times 10^{-3}$ at $a = 0.1$. Find a mechanism (tracker or coupled dark energy, or anthropic selection with an explicitly defined measure) that predicts $r$ of order one at the epoch when observers form without tuning its parameters, while staying consistent with the measured $w(z)$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-energy.sn-calibration-systematics",
      "fields": {
        "precise": {
          "text": "The DESI DR2 preference for $w0-wa$ ranges from about $2.8\\text{ to }4.2\\sigma$ across Pantheon+, Union3 and DES-Y5, and the 2025 DES reanalysis (Dovekie) lowered the DES value. Determine whether a distance-modulus offset of order $0.04\\,\\mathrm{mag}$ between low-redshift ($z < 0.1$) and high-redshift supernovae, from photometric calibration, selection, or host-galaxy dust and age evolution, accounts for the signal. Answer: identification of such a systematic or a demonstration that all such offsets are below $0.01\\,\\mathrm{mag}$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-matter-identity.qcd-axion",
      "fields": {
        "precise": {
          "text": "Does a QCD axion with mass $m_a$ in roughly $10^{-6} \\text{ to } 10^{-3}\\, \\mathrm{eV}$ and photon coupling $g_a-\\gamma$ on the KSVZ or DFSZ model bands constitute $\\Omega_c$? An answer is a haloscope or helioscope detection at a fixed frequency $\\nu = m_a c^2 / h$ with the predicted coupling, or exclusion of the DFSZ band over the mass range favored by post-inflationary production.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Resonant-cavity, dielectric or plasma haloscopes scanning the $10^{-6}$ to $10^{-3}$ eV mass range at DFSZ sensitivity.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-matter-identity.sidm-cross-section",
      "fields": {
        "precise": {
          "text": "Measure the self-interaction cross section per unit mass $\\sigma/m$ ($\\mathrm{cm}^2/\\mathrm{g}$) as a function of relative velocity v from about $3 \\times 10^{6}\\ \\mathrm{cm}/\\mathrm{s}$ (dwarfs) to $10^{8}\\ \\mathrm{cm}/\\mathrm{s}$ (clusters) using dwarf rotation curves, satellite central densities, strong-lens perturbers, cluster cores and cluster mergers. Kaplinghat, Tulin and Yu (2016, PRL 116, 041302) infer about $2\\ \\mathrm{cm}^2/\\mathrm{g}$ at galaxy scales and $0.1\\ \\mathrm{cm}^2/\\mathrm{g}$ at cluster scales. An answer is a nonzero $\\sigma/m(v)$ detected at more than $3\\sigma$, or an upper bound below $0.1\\ \\mathrm{cm}^2/\\mathrm{g}$ at dwarf velocities.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "The dense $10^{6}\\,M_{\\mathrm{sun}}$ perturber found by gravitational imaging in JVAS B1938+666 (2025) has been interpreted as a core-collapsed self-interacting halo, an interpretation that is debated.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.dark-matter-identity.wimp-thermal-relic",
      "fields": {
        "precise": {
          "text": "Does a particle of mass $1\\,\\mathrm{GeV}\\text{ to }100\\,\\mathrm{TeV}$, produced by thermal freeze-out with annihilation cross section $\\langle \\sigma v\\rangle \\sim 3 \\times 10^{-26}\\,\\mathrm{cm}^{3}/\\mathrm{s}$, make up $\\Omega_c$? Answer yes (a detection of nuclear recoils, annihilation products or collider production consistent with the thermal cross section) or no for named benchmarks: exclusion of Higgs-portal and Z-portal thermal relics by direct detection, and of the pure wino ($\\sim 2.9\\,\\mathrm{TeV}$) and pure Higgsino ($\\sim 1.1\\,\\mathrm{TeV}$) thermal relics by gamma-ray line and continuum searches from the Galactic Center. Thermal relics with loop-suppressed nuclear couplings (pure Higgsino, $\\sigma_{\\mathrm{SI}} \\sim 10^{-49}\\text{ to }10^{-48}\\,\\mathrm{cm}^{2}$) lie at or below the xenon neutrino background floor, so direct detection alone cannot close the question.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "LZ (2025, 4.2 tonne-years) found no excess and excluded spin-independent WIMP-nucleon cross sections above $2.2 \\times 10^{-48}\\,\\mathrm{cm}^{2}$ at 40 GeV (90 percent confidence).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.galaxy-scale-dark-matter.rar-origin",
      "fields": {
        "precise": {
          "text": "The radial acceleration relation $g_{\\mathrm{obs}} = g_{\\mathrm{bar}} / (1 - \\exp(-\\sqrt{g_{\\mathrm{bar}} / a0}))$ with $a0 \\sim 1.2 \\times 10^{-8}\\ \\mathrm{cm}/\\mathrm{s}^{2}$ fits about 150 SPARC rotation curves with small scatter, and the baryonic Tully-Fisher relation $M_{b}$ proportional to $V_{\\mathrm{flat}}^{4}$ holds over 5 decades in mass. Explain whether LCDM galaxy formation produces one relation with a single a0 and the observed small scatter, or whether the relation signals modified dynamics or a dark matter coupling to baryons.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.galaxy-scale-dark-matter.subhalo-mass-function",
      "fields": {
        "title": {
          "text": "Does the halo mass function continue below $10^{8}\\,\\text{solar masses}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Measure the subhalo and line-of-sight halo mass function $dn/dM$ over $M = 10^{6}\\text{ to }10^{9}\\ M_{\\mathrm{sun}}$. CDM predicts dn/dM ~ M^-1.9 with no cutoff above $\\sim 10^{-6}\\ M_{\\mathrm{sun}}$; warm, fuzzy or interacting dark matter predict suppression below a half-mode mass $M_{\\mathrm{hm}}$. An answer is a measured amplitude and slope or a bound on $M_{\\mathrm{hm}}$ from strong-lens flux ratios, gravitational imaging and stellar-stream gaps, with the density profiles of detected clumps.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "A $10^{6}\\,M_{\\mathrm{sun}}$ dark object was detected by gravitational imaging in JVAS B1938+666 (Powell et al. 2025, arXiv:2510.07382); its high central density is debated as CDM versus core-collapsed self-interacting dark matter.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.galaxy-scale-dark-matter.wide-binary-test",
      "fields": {
        "precise": {
          "text": "For Gaia wide binaries with internal Newtonian accelerations $g_N$ below $\\sim 10^{-8}\\ \\mathrm{cm}/\\mathrm{s}^2$ (projected separations above about 5000 to 7000 AU for solar-mass pairs), measure $\\gamma = G_{\\mathrm{eff}} / G$ from the distribution of relative velocities, accounting for hidden triple companions, projection and eccentricities. MOND with the Milky Way external field effect predicts $\\gamma \\sim 1.4$; Newtonian gravity predicts $\\gamma = 1$. An answer is $\\gamma$ with uncertainty below 0.05.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.hubble-tension.early-universe-fix",
      "fields": {
        "precise": {
          "text": "Determine whether any model that reduces the sound horizon $r_d$ by $\\sim 7\\%$ (early dark energy, extra radiation $\\Delta N_{\\mathrm{eff}}$, varying electron mass, primordial magnetic fields) fits Planck, ACT DR6 and SPT-3G CMB spectra plus DESI DR2 BAO with $h \\ge 0.72$ and total $\\chi^2$ no worse than LCDM. Answer yes with an explicit model or no with a general argument.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.hubble-tension.origin",
      "fields": {
        "precise": {
          "text": "Write $H0 = h x 3.24 \\times 10^{-18}\\ \\mathrm{s}^{-1}$. The SH0ES Cepheid plus type Ia supernova ladder gives $h = 0.730 \\pm 0.010$, while Planck CMB in LCDM gives $h = 0.674 \\pm 0.005$. Identify whether the discrepancy comes from distance-ladder systematics, from physics before recombination that shrinks the sound horizon, or from late-time physics, with a model that fits all data at least as well as LCDM.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.inflation.local-non-gaussianity",
      "fields": {
        "precise": {
          "text": "Measure the local bispectrum amplitude $f_{\\mathrm{NL}}^{\\mathrm{local}}$; Planck 2018 gives $f_{\\mathrm{NL}}^{\\mathrm{local}} = -0.9 \\pm 5.1$. Single-field inflation predicts $\\left|f_{\\mathrm{NL}}^{\\mathrm{local}}\\right| \\ll 1$ in the squeezed limit; many multi-field models give $\\left|f_{\\mathrm{NL}}^{\\mathrm{local}}\\right| \\ge 1$. An answer is $f_{\\mathrm{NL}}^{\\mathrm{local}}$ with $\\sigma$ below 0.5 from scale-dependent galaxy bias and CMB.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.inflation.tensor-to-scalar-ratio",
      "fields": {
        "precise": {
          "text": "Measure the tensor-to-scalar ratio r at pivot $k = 0.05\\ \\mathrm{Mpc}^{-1}$, which fixes the inflation energy scale $V^{(1/4)} \\sim 1.04 \\times 10^{16}\\ \\mathrm{GeV}\\ (r / 0.01)^{(1/4)}$. Current bound $r < 0.036$ (95 percent, BICEP/Keck 2021), $r < 0.038$ with ACT DR6. An answer is a detection or a bound $r < 0.001$ after delensing and foreground separation.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.lithium-problem.lithium7-deficit",
      "fields": {
        "precise": {
          "text": "Standard BBN with the Planck baryon density $\\eta \\sim 6.1 \\times 10^{-10}$ predicts $\\mathrm{Li}/\\mathrm{H} \\sim 5 \\times 10^{-10}$, while the Spite plateau of metal-poor dwarfs ($[\\mathrm{Fe}/\\mathrm{H}] < -1.5$) gives $\\mathrm{Li}/\\mathrm{H} \\sim 1.6 \\times 10^{-10}$, a factor 3 to 4 at more than $5\\,\\sigma$. Identify the cause: stellar depletion by atomic diffusion and mixing, nuclear-rate errors, or non-standard physics (decaying particles, varying constants).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.lithium-problem.stellar-depletion",
      "fields": {
        "precise": {
          "text": "For stars of $0.6 \\text{ to } 0.8\\,M_{\\mathrm{sun}}$ with $[\\mathrm{Fe}/\\mathrm{H}] < -2$ and ages $12 \\text{ to } 13\\,\\mathrm{Gyr}$, determine whether atomic diffusion plus convective-boundary and rotational mixing reduces surface $\\mathrm{Li}/\\mathrm{H}$ from $\\sim 5 \\times 10^{-10}$ to $\\sim 1.6 \\times 10^{-10}$ with star-to-star dispersion below $0.1\\,\\mathrm{dex}$, and reproduces the drop in Li below $[\\mathrm{Fe}/\\mathrm{H}] \\sim -3$. Answer yes with a model calibrated on globular-cluster turnoff and subgiant stars, or no.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.primordial-black-holes.asteroid-window",
      "fields": {
        "precise": {
          "text": "For primordial black holes with masses $M = 10^{17} \\text{ to } 10^{22}\\,\\mathrm{g}$, no current constraint excludes a dark-matter fraction $f_{\\mathrm{PBH}} = \\Omega_{\\mathrm{PBH}} / \\Omega_c = 1$. Determine whether $f_{\\mathrm{PBH}} = 1$ is allowed anywhere in this window, via detection (Hawking evaporation products at the light end, femtolensing or microlensing of stars and gamma-ray bursts, dynamical capture in stars) or exclusion of $f_{\\mathrm{PBH}} = 1$ across the whole window for monochromatic and extended mass functions.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Microlensing surveys and MeV $\\gamma$-ray observations sensitive enough to probe $f_{\\mathrm{PBH}} < 1$ throughout $10^{17}$ to $10^{22}$ g.",
          "how": [
            "outside:e-notation"
          ]
        },
        "status_note": {
          "text": "2026 reviews still list $10^{17}\\ \\text{to}\\ 10^{22}\\,\\mathrm{g}$ as a window where $f_{\\mathrm{PBH}} = 1$ is allowed.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.primordial-black-holes.earth-mass-events",
      "fields": {
        "precise": {
          "text": "OGLE bulge data contain 6 ultrashort events that Niikura et al. (2019, arXiv:1901.07120) reproduce with Earth-mass PBHs forming about a percent of dark matter, while MOA (Sumi et al. 2023, arXiv:2303.08280) attributes such events to about 21 free-floating planets per star. Determine $f_{\\mathrm{PBH}} = \\Omega_{\\mathrm{PBH}} / \\Omega_{c}$ for $M = 10^{-7}\\ \\text{to}\\ 10^{-5}\\ M_{\\mathrm{sun}}$ ($2 \\times 10^{26}\\ \\text{to}\\ 2 \\times 10^{28}\\ \\mathrm{g}$) by separating lens populations through event-rate dependence on direction (bulge, disk, halo, lines of sight to the LMC and M31) and through lens-distance information.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "Mroz et al. (2024, Nature 632, 749) bound $f_{\\mathrm{PBH}} < 0.1$ for $1.3 \\times 10^{-5} \\text{ to } 860\\,M_{\\mathrm{sun}}$ toward the LMC, leaving the Earth-mass range less constrained.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.primordial-black-holes.merger-fraction",
      "fields": {
        "status_note": {
          "text": "Mroz et al. (2024) bound compact halo objects of $1.8 \\times 10^{-4} \\text{ to } 6.3\\,M_{\\mathrm{sun}}$ below 1 percent of dark matter; the O4 candidate S251112cm (2025), found by the sub-solar-mass search, has low significance (false-alarm rate about 1 per 6 yr), and no confident sub-solar-mass merger exists.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.primordial-black-holes.small-scale-power",
      "fields": {
        "precise": {
          "text": "The curvature power spectrum is $P_{\\zeta} \\sim 2.1 \\times 10^{-9}$ at $k = 0.05\\,\\mathrm{Mpc}^{-1}$, while a cosmologically relevant PBH abundance needs $P_{\\zeta} \\sim 10^{-2}$ at the scale entering the horizon at formation. Measure or bound $P_{\\zeta}(k)$ for $k > 1\\,\\mathrm{Mpc}^{-1}$ using CMB spectral distortions (the COBE/FIRAS mu-distortion limit is about three orders of magnitude stronger than the PBH limit at $k \\sim 10^{1} \\text{ to } 10^{4}\\,\\mathrm{Mpc}^{-1}$, Chluba, Erickcek and Ben-Dayan 2012), scalar-induced gravitational waves in pulsar-timing, LISA and ground-based bands, and ultracompact minihalos. An answer is a detected enhancement or an upper bound below the PBH-forming level at each $k$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.structure-growth-neutrino-mass.growth-index",
      "fields": {
        "precise": {
          "text": "Measure the growth index $\\gamma$ in $f(z) = \\Omega_m(z)^\\gamma$, where $f = d\\mathrm{ln}(\\delta)/d\\mathrm{ln}(a)$, over $0 < z < 2$ from redshift-space distortions, peculiar velocities and lensing; general relativity with LCDM gives $\\gamma \\sim 0.55$. An answer is $\\gamma$ with uncertainty below 0.02 and a test of its redshift dependence.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "cosmo.structure-growth-neutrino-mass.neutrino-mass-consistency",
      "fields": {
        "precise": {
          "text": "In LCDM, DESI DR2 BAO plus CMB gives $\\sum\\, m_\\nu < 0.064\\,\\mathrm{eV}$ (95 percent; 0.053 eV with the Feldman-Cousins construction), while oscillations require $\\sum\\, m_\\nu \\ge 0.059\\,\\mathrm{eV}$ (normal ordering) or $\\ge 0.10\\,\\mathrm{eV}$ (inverted ordering), and the posterior extended to an effective negative mass peaks below zero. Determine whether a positive $\\sum\\, m_\\nu \\ge 0.059\\,\\mathrm{eV}$ is consistent with the data, or whether the deficit requires new physics (evolving dark energy, modified lensing amplitude, neutrino decay or non-standard interactions) or unrecognized systematics.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.atmospheric-electricity.cloud-charging",
      "fields": {
        "precise": {
          "text": "Laboratory experiments since the 1970s show that rebounding collisions between ice crystals and riming graupel transfer charges of order $3 \\times 10^{-6} \\text{ to } 3 \\times 10^{-4}\\,\\mathrm{statC}$ per collision, with the sign of graupel charge reversing near $253 \\text{ to } 263\\,\\mathrm{K}$ depending on liquid water content (review: Saunders, Space Science Reviews 2008, https://doi.org/10.1007/s11214-008-9345-0). Identify the microphysical mechanism (relative vapor growth rates of the colliding surfaces, mass transfer through the quasi-liquid surface layer, ionic impurities) and derive a charge-transfer law as a function of temperature, liquid water content, impact speed and particle size. An answer is a physical law that reproduces the laboratory charging diagrams and the observed tripole charge structure of storms.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.atmospheric-electricity.silicon-vapor-test",
      "fields": {
        "precise": {
          "text": "In the silicon-vapor model, a ground strike reduces $\\mathrm{SiO_2}$ to Si vapor that condenses into nanoparticle networks which oxidize slowly. Determine whether this model, with realistic soil composition and lightning energy deposition, reproduces observed lifetimes of seconds, sizes near 20 cm, buoyancy and Si, Fe, Ca line strengths. An answer is a quantitative comparison yielding consistency or exclusion.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.climate-sensitivity.aerosol-forcing",
      "fields": {
        "precise": {
          "text": "The industrial-era total aerosol effective radiative forcing has a 68 percent range of about $-1.6 \\times 10^{3} \\text{ to } -0.65 \\times 10^{3}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2)$ (Bellouin and coauthors, Reviews of Geophysics 2020, https://doi.org/10.1029/2019RG000660), dominated by aerosol-cloud interactions (droplet number, liquid-water-path and cloud-fraction adjustments). Determine this forcing with a 68 percent range narrower than about $4 \\times 10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2)$. An answer is a value supported by process-level observations of cloud adjustments and consistent with the historical and interhemispheric temperature record.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.climate-sensitivity.anvil-feedback",
      "fields": {
        "precise": {
          "text": "The tropical anvil cloud area feedback was assessed at about $-2 \\times 10^{2} \\pm 2 \\times 10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2\\,\\mathrm{K})$ (Sherwood and coauthors 2020), while the iris hypothesis (Lindzen and coauthors 2001) argued for a much more negative value. Determine the global anvil-area feedback and its mechanism (stability iris, changes in convective aggregation, anvil lifetime and microphysics) with uncertainty below about $10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2\\,\\mathrm{K})$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.climate-sensitivity.ecs-value",
      "fields": {
        "plain": {
          "text": "Doubling $\\mathrm{CO_2}$ will warm Earth by somewhere around 2.5 to 4 degrees once the oceans catch up. Narrowing that range has proved hard for decades.",
          "how": [
            "outside:chemical"
          ]
        },
        "precise": {
          "text": "Equilibrium climate sensitivity (ECS) is the equilibrium global-mean surface air temperature change for doubled $\\mathrm{CO_2}$ (forcing about $4\\mathrm{e}3\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^{2})$). The 2020 multi-evidence assessment gives a 66 percent range of about $2.6\\ \\text{to}\\ 3.9\\,\\mathrm{K}$ and the 2021 IPCC assessment a likely range of $2.5\\ \\text{to}\\ 4\\,\\mathrm{K}$. An answer is a 66 percent range narrower than $1\\,\\mathrm{K}$ consistent with process, historical and paleoclimate evidence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.climate-sensitivity.hot-models",
      "fields": {
        "plain": {
          "text": "Several recent climate models warm by more than 5 degrees for doubled $\\mathrm{CO_2}$. Past climates such as the last ice age may show this is too much.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.climate-sensitivity.low-cloud-feedback",
      "fields": {
        "precise": {
          "text": "Determine the global low-cloud feedback parameter (stratocumulus and trade cumulus over the subtropical oceans) in $\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^{2}\\,\\mathrm{K})$; current assessments center near $+2 \\times 10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^{2}\\,\\mathrm{K})$ with large uncertainty. An answer is a value with uncertainty below about $10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^{2}\\,\\mathrm{K})$ supported by large-eddy simulations and observed cloud-controlling-factor relations.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earth-moon-origin.isotopic-crisis",
      "fields": {
        "precise": {
          "text": "Canonical giant-impact simulations (impactor mass about 0.1 Earth masses) place mostly impactor material in the protolunar disk, yet the Earth-Moon difference in $\\Delta-17O$ is about $-1 \\pm 5\\ \\mathrm{ppm}$, Ti and Cr isotopes also match, and $182\\mathrm{W}$ matches once the different amounts of late-accreted material on Earth and Moon are corrected for. Identify the formation scenario that jointly reproduces the isotopic match, the angular momentum, the lunar mass and the small lunar core. An answer is a simulated scenario meeting all four constraints with plausible initial conditions.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earth-moon-origin.moon-age",
      "fields": {
        "precise": {
          "text": "The oldest lunar zircons give ages near 4.46 to 4.51 Ga, whereas many ferroan anorthosites and lunar magma-ocean model ages cluster near 4.35 Ga. Determine the age of the Moon-forming impact and whether the 4.35 Ga cluster records formation or a later tidally driven remelting of an older Moon. An answer is an impact age with uncertainty below about $2 \\times 10^{7}$ yr consistent with lunar and terrestrial Hf-W, Sm-Nd and U-Pb chronometers.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earth-moon-origin.water-inventory",
      "fields": {
        "precise": {
          "text": "Determine the bulk-Earth hydrogen inventory expressed in ocean masses (1 ocean is about $1.4 \\times 10^{24}\\,\\mathrm{g}$ of water), split among oceans, mantle and core. Mantle estimates range from below one to a few oceans and core estimates up to tens of oceans equivalent depending on metal-silicate partitioning. An answer is each reservoir's content with uncertainty below a factor of two.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earth-moon-origin.water-source",
      "fields": {
        "precise": {
          "text": "Earth's ocean $\\mathrm{D}/\\mathrm{H}$ is about $1.5 \\times 10^{-4}$, similar to CI and CM carbonaceous chondrites and to enstatite chondrites, while nebular hydrogen has $\\mathrm{D}/\\mathrm{H}$ near $2 \\times 10^{-5}$. Determine the fractional contributions of carbonaceous material, inner-disk (enstatite-like) material, nebular ingassing and comets to bulk Earth hydrogen, and whether delivery preceded or followed the Moon-forming impact. An answer is a mixing solution consistent with H, N, noble gas and nucleosynthetic isotope data.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earthquake-physics.dynamic-weakening",
      "fields": {
        "precise": {
          "text": "At slip rates near $10^{2}\\,\\mathrm{cm}/\\mathrm{s}$, laboratory friction falls to coefficients of about 0.1 to 0.3. Identify which mechanism (flash heating at asperity contacts, thermal pressurization of pore fluid, melt lubrication, nanopowder or silica-gel lubrication) controls coseismic shear stress at seismogenic depths on natural faults, and its dependence on slip and slip rate. An answer is a constitutive law validated against natural fault-zone observations.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earthquake-physics.heat-flow-paradox",
      "fields": {
        "precise": {
          "text": "The absence of a frictional heat-flow anomaly over the San Andreas fault implies mean shear stress below about $2 \\times 10^{8}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$, while Byerlee friction (coefficient 0.6 to 0.85) at seismogenic depth predicts about $10^{9}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$. Determine whether mature faults are statically weak (weak clay minerals, high pore pressure) or only dynamically weak during slip. An answer is a measured in situ shear stress and friction profile consistent with heat flow and stress orientation data. The residual question concerns locked, seismogenic fault segments.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.earthquake-physics.slow-slip-control",
      "fields": {
        "precise": {
          "text": "Slow slip events and tectonic tremor at subduction zones move at slip rates of order $10^{-6} \\text{ to } 10^{-5}\\,\\mathrm{cm/s}$, roughly $10 \\text{ to } 100$ times the plate rate and about $10^{7} \\text{ to } 10^{8}$ times slower than earthquake slip (near $10^{2}\\,\\mathrm{cm/s}$). Identify the physical control: near-neutral rate-and-state frictional stability ($a - b \\text{ near } 0$) with high pore-fluid pressure, dilatancy strengthening, mixed frictional-viscous rheology, or fault-zone heterogeneity, and whether and when slow slip triggers large earthquakes. An answer is a constitutive model, tested against laboratory data, that reproduces the observed moment-duration scaling, recurrence and tremor of slow slip (review: Burgmann, EPSL 2018, https://doi.org/10.1016/j.epsl.2018.04.062).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.geodynamo.early-dynamo-power",
      "fields": {
        "precise": {
          "text": "Paleointensity data indicate a dynamo since at least about $3.4 \\text{ to } 3.5\\,\\mathrm{Ga}$, with possible records to about $3.7\\,\\mathrm{Ga}$ from Isua, Greenland (Nichols and coauthors, JGR Solid Earth 2024, https://doi.org/10.1029/2023JB027706). With core thermal conductivity $k$ of order $10^{7}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}\\,\\mathrm{K})$ or higher, the adiabatic heat flow can exceed $Q_{\\mathrm{cmb}}$ before inner-core nucleation (the new core paradox). Identify which source supplied the needed entropy: precipitation of MgO, $\\mathrm{SiO_2}$ or FeO, a basal magma-ocean dynamo, tidal or precessional forcing, or a lower $k$. An answer is a thermal and chemical core history that satisfies the paleointensity record and mineral-physics constraints.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.geodynamo.reversal-forecast",
      "fields": {
        "precise": {
          "text": "Using satellite-era, historical and archeomagnetic field models (axial dipole decline since about 1840, growth of the South Atlantic Anomaly), determine whether any observable statistic of the core-surface field forecasts a reversal or excursion within $10^{3}$ to $10^{4}$ yr with skill above chance. An answer is a forecasting statistic validated retrospectively on paleomagnetic records and on long dynamo simulations, or a demonstration, on long reversing dynamo simulations, that no core-surface statistic has skill above chance at these lead times.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.geodynamo.reversal-trigger",
      "fields": {
        "title": {
          "text": "What triggers geomagnetic polarity reversals and sets their rate?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "The axial dipole reverses irregularly, at a mean rate of roughly 4 to 5 per Myr over the last few Myr and essentially zero during superchrons such as the Cretaceous Normal Superchron (about 121 to 83 Ma). Identify the magnetohydrodynamic mechanism in the rotating, convecting outer core (Ekman number $E \\sim 10^{-15}$, magnetic Prandtl number $\\mathrm{Pm} \\sim 10^{-6}$) that initiates reversals and controls their rate. An answer is a mechanism demonstrated in dynamo simulations at Earth-like parameter ratios that reproduces the observed reversal statistics (rate, duration of transitions, excursion frequency).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.geodynamo.scaling-regime",
      "fields": {
        "precise": {
          "text": "Simulations reach $E \\sim 10^{-7} \\text{ to } 10^{-8}$ versus Earth's $E \\sim 10^{-15}$. Determine whether a magnetostrophic asymptotic regime exists in which field strength, flow length scales and secular variation become independent of viscosity, and whether present simulations lie in it. An answer is scaling laws verified over several decades of $E$ with the predicted exponents and Earth-extrapolated values matching observed field strength and secular variation.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.geodynamo.superchron-control",
      "fields": {
        "precise": {
          "text": "Test whether time variations of the total core-mantle boundary heat flow $Q_{\\mathrm{cmb}}$ and its lateral pattern over $10^{8}$ yr, taken from mantle-convection reconstructions, quantitatively reproduce the observed reversal-rate history including the Cretaceous Normal Superchron. An answer is either dynamo simulations driven by reconstructed CMB heat-flux histories that match the reversal-rate record, or a demonstration that rate swings of this size arise intrinsically at fixed boundary conditions.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.giant-planet-interiors.jupiter-dilute-core",
      "fields": {
        "precise": {
          "text": "Determine the heavy-element mass fraction profile $Z(r)$ in Jupiter, including the radial extent of the dilute core (models range from about 0.3 to 0.6 Jupiter radii), from Juno even zonal gravity harmonics $J_2n$, the tidal Love number $k_{2}$ and atmospheric composition. An answer is $Z(r)$ with uncertainty bands consistent with all data and with hydrogen-helium equation-of-state uncertainty propagated.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.giant-planet-interiors.metallicity-inversion",
      "fields": {
        "precise": {
          "text": "The Galileo probe found atmospheric heavy-element enrichment of roughly three times solar, while many Juno-fitting interior models require a lower $Z$ in the outer envelope, implying an inverted $Z$ gradient. Determine whether this tension arises from hydrogen-helium equation-of-state errors, deep wind effects on gravity, or a real compositional inversion. An answer is an interior model with atmospheric $Z$ that fits $J_2n$ and $k_2$, or a demonstration that the inversion is required.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.giant-planet-interiors.saturn-rings-age",
      "fields": {
        "precise": {
          "text": "Cassini measured a ring mass of about $1.5 \\times 10^{22}\\ \\mathrm{g}$, a non-icy fraction of a few percent and the micrometeoroid influx, giving an exposure age below a few hundred Myr (Kempf and coauthors, 2023). Determine the ring age by resolving whether impact vaporization, ballistic transport, gravitational focusing and space weathering allow nearly pure ice rings of age about $4.5\\ \\mathrm{Gyr}$. An answer is an age estimate with uncertainty that survives the stated physical uncertainties.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.giant-planet-interiors.uranus-heat",
      "fields": {
        "precise": {
          "text": "Neptune's internal heat flux is about $4 \\times 10^{2}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2)$ (Voyager-era estimate), whereas a 2025 full-orbit energy-budget analysis gives $78\\pm 18\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}^2)$ for Uranus (Wang and coauthors, GRL 2025, https://doi.org/10.1029/2025GL115660). Determine the cause: a stably stratified interior with composition gradients that suppresses convection, early heat loss after a giant impact, or a different bulk composition. An answer is an interior and evolution model reproducing both planets' present fluxes, radii and gravity harmonics.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.inner-core.core-conductivity",
      "fields": {
        "precise": {
          "text": "Determine the thermal conductivity $k$ of the outer-core Fe-Ni-light-element liquid at $P \\sim 1.36 \\times 10^{12}\\,\\mathrm{dyn}/\\mathrm{cm}^2$ and $T \\sim 4000\\,\\mathrm{K}$. Ab initio calculations give $k$ of order $10^{7}\\ \\text{to}\\ 2.5 \\times 10^{7}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}\\,\\mathrm{K})$ while some laser-heated diamond-anvil measurements give values near $3 \\times 10^{6}\\,\\mathrm{erg}/(\\mathrm{s}\\,\\mathrm{cm}\\,\\mathrm{K})$. An answer is $k$ with about 20 percent uncertainty including light-element and electron-electron scattering contributions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.mantle-structure.primordial-reservoir",
      "fields": {
        "precise": {
          "text": "Ocean-island basalts show $3\\mathrm{He}/4\\mathrm{He}$ up to about 50 times the atmospheric ratio and negative $\\mu-182W$ anomalies indicating reservoirs isolated since about $4.5\\ \\mathrm{Ga}$. Identify the host: LLSVPs, ultra-low-velocity zones, bridgmanite-enriched domains, or exchange with the core. An answer is a reservoir whose survival is shown dynamically and whose geochemical predictions match observed isotope correlations.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.mantle-structure.radiogenic-heat",
      "fields": {
        "precise": {
          "text": "Surface heat loss is about $4.6 \\times 10^{20}\\,\\mathrm{erg}/\\mathrm{s}$. Borexino (Physical Review D 2020, arXiv:1909.02257) inferred mantle radiogenic power $2.5 \\times 10^{20}\\,(+1.1 \\times 10^{20}, -1.0 \\times 10^{20})\\,\\mathrm{erg}/\\mathrm{s}$, total radiogenic power $3.8 \\times 10^{20}\\,(+1.4 \\times 10^{20}, -1.3 \\times 10^{20})\\,\\mathrm{erg}/\\mathrm{s}$ and a convective Urey ratio (mantle radiogenic heat over mantle heat loss) of $0.78\\,(+0.41, -0.28)$, while bulk-silicate-Earth composition models span roughly $10^{20}\\ \\text{to}\\ 3 \\times 10^{20}\\,\\mathrm{erg}/\\mathrm{s}$ of total radiogenic power. Determine mantle radiogenic power with uncertainty below about $3 \\times 10^{19}\\,\\mathrm{erg}/\\mathrm{s}$ and identify which composition model holds.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.paleoclimate-puzzles.early-mars-warmth",
      "fields": {
        "precise": {
          "text": "For Noachian to early Hesperian Mars (about $3.8\\ \\text{to}\\ 3.5\\,\\mathrm{Gyr}$ ago, insolation $\\sim 0.32\\,S_0$ relative to modern Earth) determine whether surface runoff required sustained warm conditions (mean $T$ above $273\\,\\mathrm{K}$) or episodic warming, and identify the forcing: $\\mathrm{CO_2}$-$\\mathrm{H_2}$ or $\\mathrm{CO_2}$-$\\mathrm{CH_4}$ collision-induced absorption, cirrus clouds, impacts or volcanic outgassing. An answer specifies atmospheric composition, pressure and duration consistent with valley-network and lake-sediment volumes and with surviving carbonate inventories.",
          "how": [
            "outside:chemical"
          ]
        },
        "settled_by": {
          "text": "A climate scenario whose required $\\mathrm{H_2}$ or $\\mathrm{CH_4}$ sources, surface pressure and warm-period duration match sediment volumes and the measured carbonate and atmospheric-loss record.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.paleoclimate-puzzles.faint-young-sun",
      "fields": {
        "precise": {
          "text": "For Archean Earth (3.8 to 2.5 Gyr ago) with solar constant $S \\sim 0.75 S_{0}$ at 3.8 Gyr ago rising to $\\sim 0.82 S_{0}$ at 2.5 Gyr ago ($S_{0} = 1.36 \\times 10^{6}\\ \\mathrm{erg}\\ \\mathrm{cm}^{-2}\\ \\mathrm{s}^{-1}$), identify the combination of greenhouse gases ($\\mathrm{CO_2}$, $\\mathrm{CH_4}$, $\\mathrm{N_2}$ pressure broadening, $\\mathrm{H_2}$), cloud and surface albedo changes that yields global mean surface temperature above freezing while satisfying geochemical limits on pCO2 from paleosols and marine carbonates. An answer is a mechanism with an atmospheric composition consistent with all proxy bounds in a 3D climate model.",
          "how": [
            "inside:x-times",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.paleoclimate-puzzles.glacial-co2",
      "fields": {
        "title": {
          "text": "What lowered atmospheric $\\mathrm{CO_2}$ by about $90\\,\\mathrm{ppm}$ in glacial times?",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        },
        "precise": {
          "text": "Quantify the contributions of ocean temperature and solubility, Southern Ocean sea-ice capping and stratification, iron fertilization of the biological pump, carbonate compensation and terrestrial carbon to the roughly $90\\,\\mathrm{ppm}$ glacial-interglacial $p\\mathrm{CO}2$ change, with a budget that closes within proxy uncertainty. An answer is a quantitative carbon budget consistent with deep-ocean carbon-14 ages, $\\delta-13\\mathrm{C}$ and carbonate-ion proxies at the Last Glacial Maximum.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "An Earth-system model simulation of the Last Glacial Maximum that matches ice-core $p\\mathrm{CO}2$ together with radiocarbon, $\\delta-13\\mathrm{C}$ and carbonate-ion proxy fields.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.paleoclimate-puzzles.mid-pleistocene-transition",
      "fields": {
        "precise": {
          "text": "Between about 1.25 and 0.7 Myr ago the dominant period of benthic $\\delta-18\\mathrm{O}$ changed from 41 kyr (obliquity) to roughly 100 kyr with larger amplitude, with no corresponding change in orbital forcing. Identify the internal change (removal of deformable regolith under ice sheets, long-term $\\mathrm{CO_2}$ decline, Southern Ocean stratification, or a threshold in ice-sheet dynamics) and show it reproduces the period change and the sawtooth shape in a model forced only by insolation.",
          "how": [
            "outside:chemical",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.paleoclimate-puzzles.snowball-onset-exit",
      "fields": {
        "precise": {
          "text": "For the Sturtian (about 717 to 660 Myr ago) and Marinoan (ending about 635 Myr ago) glaciations, determine the trigger for crossing the ice-albedo bifurcation ($\\mathrm{CO_2}$ drawdown by weathering of low-latitude basalt provinces, volcanic aerosols, or other) and the deglaciation pathway, including the $pCO2$ at which a globally glaciated state with dust-darkened ice becomes unstable. An answer is a quantified trigger and exit $pCO2$ consistent with the geochronology of glacial durations of order $10^7$ yr and with cap-carbonate geochemistry.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.planetary-dynamos.ganymede-dynamo",
      "fields": {
        "precise": {
          "text": "Galileo detected an intrinsic dipole with surface equatorial strength near $7 \\times 10^{-3}$ G. Identify the power source that keeps Ganymede's Fe-FeS core convecting after 4.5 Gyr: iron snow, FeS crystallization, compositional convection, or heat from past tidal heating during resonance passage. An answer is a thermal-chemical evolution model producing a present dynamo of the observed strength.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.planetary-dynamos.lunar-dynamo",
      "fields": {
        "status_note": {
          "text": "Narrett and coauthors 2025 (Science Advances, https://doi.org/10.1126/sciadv.adr7401) show that basin-forming impact plasmas could amplify a weak dynamo field of about $0.02\\,\\mathrm{G}$ to about $0.4\\,\\mathrm{G}$ near the basin antipode, which may explain the strong paleointensities without a strong dynamo; contested.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.planetary-dynamos.mercury-weak-field",
      "fields": {
        "precise": {
          "text": "MESSENGER found an axial dipole field with surface equatorial strength near $2 \\times 10^{-3}$ G whose magnetic equator is offset about 0.2 Mercury radii north. Identify the core state (dynamo beneath a stably stratified layer, iron-snow regime, thin-shell convection) that reproduces both the weakness and the offset. An answer is a dynamo model fitting the measured low-degree Gauss coefficients and their secular variation.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.plate-tectonics.yield-stress-gap",
      "fields": {
        "precise": {
          "text": "Mantle convection models give plate-like behavior only for lithospheric yield stresses of roughly $10^{9} \\text{ to } 3 \\times 10^{9}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$, while laboratory-derived lithospheric strength is of order $10^{10}\\,\\mathrm{dyn}/\\mathrm{cm}^{2}$. Determine whether a lab-calibrated rheology (grain damage with Zener pinning, low-temperature plasticity, fluid effects) yields plate-like convection in 3D spherical models at Earth parameters. An answer is such a model or a proof that the gap remains.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.tropical-convection.cyclone-number",
      "fields": {
        "precise": {
          "text": "Derive the global annual tropical cyclone frequency (about 85 per year) from the large-scale state, specifying whether genesis is limited by the rate of seed disturbances or by environmental conditions, and predict its sign and magnitude of change under $\\mathrm{CO_2}$ doubling. An answer is a theory or validated genesis index that reproduces present climatology and agrees with convection-permitting simulations across climates.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.venus-divergence.no-dynamo",
      "fields": {
        "precise": {
          "text": "Spacecraft limits put any intrinsic Venus dipole moment below roughly $10^{-5}$ of Earth's (approximate, from Pioneer Venus era data). Determine why the Venus core sustains no dynamo: low core-mantle heat flow under a stagnant lid with no inner-core growth, a fully liquid or fully solid core, or a compositionally stratified core formed without a late giant impact (Jacobson and coauthors, EPSL 2017, https://doi.org/10.1016/j.epsl.2017.06.023). An answer is a core state (radius, solid fraction, stratification) and core heat flow consistent with the measured tidal Love number $k_2$, the moment of inertia and a thermal history, including whether a dynamo operated in the past.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.venus-divergence.oxygen-sink",
      "fields": {
        "precise": {
          "text": "Present O+ escape rates measured from orbit (of order $10^{24}\\ \\text{to}\\ 10^{25}\\,\\mathrm{ions/s}$, approximate) remove over $4\\,\\mathrm{Gyr}$ many orders of magnitude less oxygen than an Earth ocean contains (about $1.2 \\times 10^{24}\\,\\mathrm{g}$ of oxygen in $1.4 \\times 10^{24}\\,\\mathrm{g}$ of water), and present atmospheric $\\mathrm{O_2}$ is below the ppm level. Determine the oxygen sinks: drag-off with hydrogen during an early hydrodynamic escape phase, oxidation of a magma ocean or crust, and consumption by reduced volcanic gases, and hence the maximum water inventory Venus could have lost. An answer is an oxygen budget consistent with the atmospheric $D/H$ ratio, noble gases and the oxidation state of surface rocks.",
          "how": [
            "inside:e-notation",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "earth.venus-divergence.superrotation",
      "fields": {
        "precise": {
          "text": "At cloud-top altitude (about 70 km) zonal winds reach about $10^{4}\\,\\mathrm{cm}/\\mathrm{s}$, roughly 60 times the equatorial surface rotation speed. Identify the angular-momentum balance that maintains this superrotation: thermal tides driven by solar heating of the cloud layer, the Gierasch-Rossow-Williams mechanism (mean meridional circulation plus equatorward eddy transport by planetary waves and barotropic instability), or other waves, with their contributions as a function of altitude. An answer is a quantitative angular-momentum budget, from observations or from a general circulation model, that reproduces the observed wind profile and its variability.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.2d-turbulence.enstrophy-log-correction",
      "fields": {
        "precise": {
          "text": "In the direct enstrophy cascade of forced 2D turbulence, Kraichnan (1971) predicted $E(k) = C' \\eta^{2/3} k^{-3} [\\ln(k/k_f)]^{-1/3}$, with $\\eta$ the enstrophy flux and $k_f$ the forcing wavenumber. In the limit of vanishing large-scale friction and $k/k_f \\to \\infty$, verify or refute the exponent $-1/3$ of the logarithm and determine $C'$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.cavitation.emission-mechanism",
      "fields": {
        "precise": {
          "text": "Discriminate between optically thin thermal bremsstrahlung and electron-ion recombination in a weakly ionized gas, optically thick blackbody emission from the core, and atomic or molecular line emission, by predicting together the photon number per flash ($\\sim 10^{5} \\text{ to } 10^{7}$), the spectral shape from $2 \\times 10^{-5} \\text{ to } 8 \\times 10^{-5}\\,\\mathrm{cm}$ wavelength, and the pulse width (in water about $4 \\times 10^{-11} \\text{ to } 3.5 \\times 10^{-10}\\,\\mathrm{s}$, independent of wavelength; in concentrated sulfuric acid longer, of order $10^{-9}\\,\\mathrm{s}$), using the measured values for each liquid. The answer must hold for argon and xenon bubbles in both water and sulfuric acid.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.cavitation.erosion-load",
      "fields": {
        "precise": {
          "text": "For a bubble of maximum radius $R_{\\max}$ collapsing at stand-off parameter $\\gamma = d/R_{\\max}$ from a rigid wall, determine the peak wall pressure, its duration and impulse from jet impact (jet speeds $\\sim 10^{4}\\,\\mathrm{cm/s}$ and above) versus the shock emitted at the collapse of the toroidal bubble, as functions of $\\gamma$, and which quantity correlates with measured pit formation in metals. An answer is a damage criterion in terms of $\\gamma$, $R_{\\max}$ and driving pressure that predicts pit depth and occurrence.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.cavitation.noble-gas-rectification",
      "fields": {
        "precise": {
          "text": "For single-bubble sonoluminescence in water with dissolved gas concentration $c_{\\infty}/c_0$ and noble-gas species He, Ne, Ar, Kr, Xe, predict from bubble dynamics with chemistry, heat conduction and water-vapor trapping the stable region in the ($P_a, c_{\\infty}/c_0$) plane and the light yield per flash for each gas, including the large yield increase from He to Xe. An answer is a single model that matches measured phase diagrams and yields for all five gases.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.cavitation.sbsl-peak-temperature",
      "fields": {
        "precise": {
          "text": "For a stably driven argon or air bubble in water (ambient radius $R_0 \\sim 5 \\times 10^{-4}\\,\\mathrm{cm}$, drive frequency $\\sim 2.5 \\times 10^{4}\\,\\mathrm{Hz}$, acoustic pressure amplitude $P_a \\sim 1.2\\ \\text{to}\\ 1.5\\,\\mathrm{bar}$), determine the spatially resolved peak temperature $T_{\\max}$ and gas density at collapse. Spectral fits in water give $T$ of order $6 \\times 10^{3}\\ \\text{to}\\ 2 \\times 10^{4}\\,\\mathrm{K}$, spectroscopy in concentrated sulfuric acid shows plasma signatures, and some models predict converging shocks heating a small core above $10^{5}\\,\\mathrm{K}$. An answer is a measured $T_{\\max}(r)$ with error bars, or a simulation that matches spectra, absolute photon number and pulse width simultaneously without free parameters.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.cavitation.turbulent-inception",
      "fields": {
        "precise": {
          "text": "For a turbulent shear layer, wake or tip vortex in water with nuclei size distribution $n(R)$, predict the inception cavitation number $\\sigma_i = (p_{\\infty} - p_v)/(\\rho U^2/2)$ as a function of Reynolds number Re and $n(R)$, including the empirical power laws $\\sigma_i \\sim \\mathrm{Re}^a$ ($a$ near 0.4 for tip vortices). An answer combines the statistics of pressure minima and their lifetimes in turbulent vortices with the dynamic response of nuclei (Blake critical pressure, residence time) and is validated across model and full scale.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.contact-lines.air-entrainment-threshold",
      "fields": {
        "precise": {
          "text": "For a solid plunging at speed $U$ into a liquid of viscosity $\\eta$ and surface tension $\\gamma$, surrounded by gas of viscosity $\\eta_g$ and pressure $p$, predict the critical capillary number $\\mathrm{Ca}* = \\eta U*/\\gamma$ for dynamic wetting failure, including its dependence on the viscosity ratio $\\eta_g/\\eta$, on gas rarefaction when the mean free path approaches the air-film thickness, and on the large increase of $\\mathrm{Ca}*$ when the flow pushes the liquid against the solid (curtain coating). An answer predicts $\\mathrm{Ca}*$ within experimental error for $\\eta_g/\\eta$ from $10^{-6}$ to $10^{-2}$ and across reduced gas pressures.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.contact-lines.dynamic-angle-law",
      "fields": {
        "precise": {
          "text": "Determine whether the dynamic angle $\\theta_d$ as a function of capillary number $Ca = \\eta U / \\gamma$ follows the hydrodynamic Cox-Voinov relation $\\theta_d^3 - \\theta_e^3 = 9 Ca \\ln(L/L_{\\mathrm{micro}})$, the molecular-kinetic relation $U = 2 \\kappa_0 \\lambda \\sinh(\\gamma (\\cos \\theta_e - \\cos \\theta_d) \\lambda^2 / (2 k_B T))$ with hopping frequency $\\kappa_0$ and site spacing $\\lambda$, or a combination, for advancing and receding lines. An answer is a law whose parameters are measured independently rather than fitted, valid for Ca from $10^{-6}$ to $10^{-1}$ across viscosity and wettability.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "A data set over five decades of $\\mathrm{Ca}\\ (10^{-6}\\text{ to }10^{-1})$ for liquids of widely varying viscosity on well-characterized surfaces, with $L_{\\mathrm{micro}}$, $\\kappa_{0}$ and $\\lambda$ determined from independent measurements.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.drop-impact.air-splash-mechanism",
      "fields": {
        "precise": {
          "text": "A low-viscosity drop of radius $R \\sim 0.1\\,\\mathrm{cm}$ hitting a smooth dry solid at speed $V$ of a few hundred cm/s splashes at 1 atm but not below a threshold gas pressure $P_{T}$ (Xu, Zhang, Nagel, PRL 2005). Identify the gas-mediated force that lifts the thin liquid sheet ejected near the contact line, and derive $P_{T}$(V, R, liquid viscosity, gas mean free path) together with the time and position of sheet ejection.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.drop-impact.bubble-pinch-off",
      "fields": {
        "settled_by": {
          "text": "Imaging and simulations resolving $h_{\\min}$ below about $10^{-4}\\ \\mathrm{cm}$ with controlled initial asymmetry, compared with the asymmetric perturbation theory.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.drop-impact.jet-drop-size",
      "fields": {
        "status_note": {
          "text": "Competing scaling laws proposed since 2017 differ near $\\mathrm{Oh}*$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.drop-impact.splash-threshold-scaling",
      "fields": {
        "precise": {
          "text": "Measure and predict $P_T$ as a function of liquid viscosity (about 0.3 to 10 cP), $V$, $R$ and gas molecular weight, establishing whether the gas enters only through its density, through its mean free path (rarefaction in the thin gas film), or both, and whether one scaling law covers low- and high-viscosity liquids.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.particle-turbulence.caustic-rate",
      "fields": {
        "precise": {
          "text": "Heavy particles with Stokes number $\\mathrm{St} = \\tau_p/\\tau_\\eta$ (particle response time over Kolmogorov time) form caustics where their velocity field becomes multivalued. Theory predicts a caustic formation rate $\\sim \\exp(-A/\\mathrm{St})$ at small St (Wilkinson, Mehlig, Bezuglyy 2006). Determine $A$, the prefactor and their $\\mathrm{Re}_\\lambda$ dependence in 3D Navier-Stokes turbulence.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.particle-turbulence.point-particle-modulation",
      "fields": {
        "precise": {
          "text": "Heavy point particles (diameter $d << \\eta$, $\\eta$ the Kolmogorov length) with Stokes number St and mass loading $\\Phi_m$ (particle-to-fluid mass ratio) of order 0.1 to 1 in homogeneous turbulence with two-way coupling. Determine the sign and magnitude of the change in carrier turbulent kinetic energy and dissipation rate as functions of $\\mathrm{St}, \\Phi_m, \\mathrm{Sv}\\text{ and }\\mathrm{Re}_\\lambda$, including the scale-by-scale energy exchange between phases. Answer: a predictive relation validated for St from about 0.1 to 10.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.rb-convection.prandtl-dependence",
      "fields": {
        "precise": {
          "text": "Within the ultimate regime of Rayleigh-Benard convection, determine the exponents in Nu ~ Pr^g1 Ra^g2 (up to logarithms) for $\\mathrm{Pr} << 1$ and $\\mathrm{Pr} >> 1$. Test the 2024 model prediction $\\mathrm{Nu} \\sim \\mathrm{Pr}^{1/2}\\mathrm{Ra}^{1/2}/(\\ln \\mathrm{Ra})^2$ for $\\mathrm{Pr} <\\sim 1$ and $\\mathrm{Nu} \\sim \\mathrm{Pr}^{-1/2}\\mathrm{Ra}^{1/2}/(\\ln \\mathrm{Ra})^2$ for $\\mathrm{Pr} >\\sim 1$, and its consistency with the rigorous bound $\\mathrm{Nu} <\\sim \\mathrm{Ra}^{1/3}$ (up to logarithms) for $\\mathrm{Pr} >\\sim \\mathrm{Ra}^{1/3}$ (Choffrut, Nobili, Otto 2016).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.rb-convection.rotating-diffusion-free",
      "fields": {
        "precise": {
          "text": "Rotating Rayleigh-Benard convection with Ekman number $\\mathrm{Ek}=\\nu/(2\\Omega H^{2})\\to 0$ and supercriticality $\\mathrm{Ra}\\sim=\\mathrm{Ra}\\,\\mathrm{Ek}^{4/3} >> 1$ ($\\Omega\\ \\text{rotation rate},\\ H\\ \\text{layer height}$). The diffusion-free (geostrophic turbulence) prediction is $\\mathrm{Nu} - 1 \\sim$ $\\mathrm{Ra}\\sim$$^{(3/2)}$ at fixed Pr. Determine whether this law holds in laboratory cells with sidewalls and centrifugal effects, its Prandtl-number dependence for Pr from about 0.03 to 7, and the $\\mathrm{Ra}\\sim$ at which it crosses over to non-rotating convection.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "DNS with no-slip plates and periodic sides at $\\mathrm{Pr} = 1$, $\\mathrm{Ra}\\ \\text{up to}\\ 3 \\times 10^{13}$ and $\\mathrm{Ek}\\ \\text{down to}\\ 5 \\times 10^{-9}$ show $\\mathrm{Nu} - 1 \\sim \\mathrm{Ra}\\sim^{(3/2)}$, with a steeper $\\mathrm{Ra}\\sim^{3}$ regime at lower $\\mathrm{Ra}\\sim$ (Song, Shishkina, Zhu, J. Fluid Mech. 2024); laboratory confirmation and the Pr dependence remain open.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.rb-convection.transition-onset",
      "fields": {
        "settled_by": {
          "text": "Systematic experiments in one apparatus varying $\\Gamma$, Pr and controlled boundary-layer perturbations, mapping $Ra*$ against $\\mathrm{Re}_{s}$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.rb-convection.ultimate-existence",
      "fields": {
        "precise": {
          "text": "System: Oberbeck-Boussinesq Rayleigh-Benard convection between smooth isothermal no-slip plates, Prandtl number $\\mathrm{Pr} \\sim 1$, aspect ratio $\\Gamma \\sim 1$. Quantity: Nusselt number $\\mathrm{Nu}(\\mathrm{Ra})$ as $\\mathrm{Ra} \\to \\infty$. Question: does the effective exponent $\\gamma = d \\mathrm{ln} \\mathrm{Nu} / d \\mathrm{ln} \\mathrm{Ra}$ cross over from about $1/3$ to the Kraichnan form $\\mathrm{Nu} \\sim \\mathrm{Ra}^{1/2} (\\mathrm{ln} \\mathrm{Ra})^{-c}$ at finite Ra, or does $\\mathrm{Nu} \\sim \\mathrm{Ra}^{1/3}$ persist? Answer: $\\gamma(\\mathrm{Ra})$ up to $\\mathrm{Ra} \\sim 10^{17}$ with non-Boussinesq, sidewall and plate corrections quantified.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Gottingen $\\mathrm{SF_6}$ data show a transition between $\\mathrm{Ra} \\sim 10^{13} \\text{ and } 5 \\times 10^{14}$ (He et al. 2012) and Grenoble helium data near $10^{11}$ (Chavanne et al. 1997), Oregon and Brno helium data do not; slender-cell DNS give $\\gamma \\sim 0.33$ up to $\\mathrm{Ra} \\sim 10^{15}$ (Iyer et al. 2020); a 2026 Brno uncertainty analysis shows data corrections can decide the claim (Urban et al., arXiv:2603.08811).",
          "how": [
            "inside:x-times",
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.small-scale.scalar-skewness",
      "fields": {
        "status_note": {
          "text": "At $\\mathrm{Sc} \\sim 1$ the derivative skewness stays of order 1 up to the highest $\\mathrm{Re}_{\\lambda}$ measured; DNS at $\\mathrm{Re}_{\\lambda} 140 \\text{ to } 650$ show isotropy is restored as Sc grows at fixed $\\mathrm{Re}_{\\lambda}$ (Buaria, Clay, Sreenivasan, Yeung, PRL 2021), a ramp-cliff model fitting the trend.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.strat-rot.rotating-cascade",
      "fields": {
        "precise": {
          "text": "In forced rotating turbulence with rotation rate $\\Omega$, forcing scale $\\ell_f$ and Rossby number $\\mathrm{Ro} = u_f/(2\\Omega \\ell_f)$, an upscale energy flux appears below a critical $\\mathrm{Ro}_c$. Determine $\\mathrm{Ro}_{c}$ in the limits $\\mathrm{Re} \\to \\infty$ and $\\text{domain size} \\to \\infty$, the scaling of the upscale flux fraction near $\\mathrm{Ro}_c$, and whether the transition is continuous with critical exponents or discontinuous with hysteresis.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.turbulent-combustion.cell-size-prediction",
      "fields": {
        "precise": {
          "text": "For gaseous detonations ($\\mathrm{H_2}$-$\\mathrm{O_2}$-Ar, $\\mathrm{H_2}$-air, hydrocarbon-air) at initial pressure $p_0$ and temperature $T_0$, predict the mean cell width $\\lambda$ from the detailed chemical mechanism. Empirical correlations $\\lambda = A \\Delta_I$, with $\\Delta_I$ the induction length of the one-dimensional steady detonation, need $A$ between about 10 and 50 depending on mixture. An answer predicts $\\lambda$ within 20 percent across mixtures and initial conditions with no fitted $A$.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.turbulent-combustion.self-acceleration-exponent",
      "fields": {
        "precise": {
          "text": "For an outwardly propagating premixed flame subject to the Darrieus-Landau (gas-expansion) and thermo-diffusive instabilities, determine whether the radius approaches a self-similar law $R \\sim t^{\\alpha}$ at $R/\\delta_L >\\sim 10^{4}$, the value of $\\alpha$ (field-scale correlations suggest $\\alpha = 3/2$, equivalent to a fractal front dimension $7/3$), and its dependence on expansion ratio and Lewis number. An answer is $\\alpha$ with uncertainty from simulations or experiments reaching the asymptotic range.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Large-scale simulations or large-volume experiments that reach $R/\\delta_{L}$ of $10^{4}$ or more and show a converged power law in $R(t)$.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.turbulent-combustion.unconfined-ddt",
      "fields": {
        "precise": {
          "text": "For a premixed fuel-air flame (for example stoichiometric $\\mathrm{H_2}$-air or $\\mathrm{CH_4}$-air) in homogeneous isotropic turbulence with no walls or obstacles, determine whether deflagration-to-detonation transition (DDT) occurs, and the threshold in turbulent intensity $u'/S_L$ and integral scale $L/\\delta_L$ ($S_L$ laminar flame speed, $\\delta_L$ laminar flame thickness). Test the proposed route in which the turbulent flame speed exceeds the Chapman-Jouguet deflagration speed (the fastest steady deflagration allowed by conservation laws), so pressure builds up in the flame brush and forms shocks that trigger detonation. An answer is a verified criterion for unconfined DDT as a function of mixture and turbulence.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "fluid.wall-turbulence.near-wall-peak",
      "fields": {
        "precise": {
          "text": "The inner peak of the streamwise variance $\\langle u'^2\\rangle+$ at $y+ \\sim 15$ grows roughly as $3.7 + 0.64\\ln \\mathrm{Re}_{\\tau}$ (approximately) in channel DNS for $\\mathrm{Re}_{\\tau}$ from 180 to about $10^4$. As $\\mathrm{Re}_{\\tau} \\to \\infty$, does it diverge logarithmically (attached-eddy prediction) or approach a finite limit with corrections of order $1/\\ln \\mathrm{Re}_{\\tau}$ or $\\mathrm{Re}_{\\tau}^{-1/4}$? Answer: the asymptotic form, with evidence beyond $\\mathrm{Re}_{\\tau} \\sim 10^5$ where the competing fits separate.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.analog-hawking.analog-backreaction",
      "fields": {
        "precise": {
          "text": "For a quasi-1D BEC sonic black hole, the back-reaction of the Hawking flux on the flow, to first order in the quantum depletion 1/(n_1D $\\xi$) (n_1D the linear density, $\\xi$ the healing length), has been computed as a stationary shift of the density, velocity and Mach-number profiles. Determine whether the surface gravity $\\kappa$ also drifts in time (sign and rate of $\\mathrm{d}\\kappa/\\mathrm{d}t$, and whether the evolution follows an evaporation law analogous to $\\mathrm{d}M/\\mathrm{d}t$ proportional to $-T_H^2$), and measure the predicted stationary or time-dependent profile change. An answer is a measured profile change that agrees with the computed one after three-body loss, heating and stimulated emission are subtracted.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.analog-hawking.dispersion-error-bound",
      "fields": {
        "precise": {
          "text": "Take a $1+1\\mathrm{D}$ field with dispersion $(\\omega - v(x) k)^2 = c^2 k^2 (1 + s k^2/k_d^2)$, $s = +1$ (superluminal) or $-1$ (subluminal), on a stationary flow $v(x)$ with a sonic horizon of surface gravity $\\kappa = \\left|d(v - c)/dx\\right|$ at the horizon. Compute the emitted spectrum $n(\\omega)$ and its deviation from the Planck law at $T_H = \\hbar \\kappa/(2 \\pi)$, including the cutoff frequency $\\omega_{\\max}$ and the greybody factor. An answer is a proven bound on $\\left|n(\\omega) - n_{\\mathrm{Planck}}(\\omega)\\right|$ as a function of $\\kappa/(c k_d)$ and the width $D$ of the near-horizon region, valid also for steep profiles with $\\kappa \\sim c k_d$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.analog-hawking.planck-scale-origin",
      "fields": {
        "plain": {
          "text": "Traced backwards in time, each Hawking particle came from a wave squeezed to a wavelength far below the Planck length (about $1.6 \\times 10^{-33}$ cm, the scale where gravity itself should behave quantum mechanically), where known physics fails. Which short-distance physics actually supplies these particles, and does the answer change the predicted temperature?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "In Lorentz-invariant quantum field theory on a collapse Schwarzschild geometry of mass M, an outgoing mode of frequency $\\omega \\sim T_H$ at time t after collapse had, near the horizon and as measured in a frame falling freely across it, frequency $\\sim \\omega \\exp(\\kappa t)$ with $\\kappa = c/(2 r_s)$, exceeding the Planck frequency after $t \\sim (2 r_s/c) \\ln(r_s/\\ell_P)$, $\\ell_P = (\\hbar G/c^{3})^{1/2} \\sim 1.6 \\times 10^{-33}\\,\\mathrm{cm}$. Identify the mechanism that supplies these modes (dispersion in a preferred frame, mode creation in a growing lattice, Lorentz-invariant nonlocality, or a full quantum gravity calculation) consistent with present bounds on Lorentz violation, and determine whether it yields $T_H = \\hbar c^{3}/(8 \\pi G M)$ with corrections suppressed by powers of $\\ell_P/r_s$. Formulating the question within a specified ultraviolet completion is part of the problem; an answer is the mechanism plus the leading correction to $T_H$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.bh-interior.complexity-volume",
      "fields": {
        "precise": {
          "text": "For the two-sided AdS-Schwarzschild black hole, the maximal-volume slice anchored at boundary time t grows as $V(t)\\ \\text{proportional to}\\ t$ up to times of order $\\exp(S)$. Determine whether a precisely defined boundary quantity (circuit complexity, Krylov complexity, or another) of the thermofield-double state equals $V/(G \\ell_{\\mathrm{AdS}})$ up to normalization, including saturation at $t \\sim \\exp(S)$ and the switchback response to perturbations. An answer is a boundary definition with proven matching properties or a demonstration that no unique quantity is singled out.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.bh-microstates.log-correction-match",
      "fields": {
        "precise": {
          "text": "One-loop Euclidean gravity gives $S = A c^{3}/(4 G \\hbar) + C \\ln(A/\\ell_{P}^{2}) + ...$, with $C$ fixed by the massless spectrum and the ensemble; Sen (2012) computed $C$ for Schwarzschild and Kerr in various dimensions. Reproduce $C$ from a microscopic count for a non-extremal black hole in some UV-complete theory. An answer is a microscopic derivation of $C$ agreeing with the macroscopic value.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.evaporation-backreaction.endpoint",
      "fields": {
        "plain": {
          "text": "Hawking's calculation stops working when the black hole shrinks to about $2 \\times 10^{-5}\\,\\mathrm{g}$, the Planck mass. The options include complete disappearance into radiation, a stable tiny leftover, a white hole, or a disconnected baby universe.",
          "how": [
            "inside:x-times"
          ]
        },
        "precise": {
          "text": "For a Schwarzschild black hole evaporating from $M \\gg m_P=\\sqrt{\\hbar c/G}$, approximately $2.2 \\times 10^{-5}\\,\\mathrm{g}$, determine the final state at $M \\sim m_P$: complete evaporation with a pure final radiation state, a stable or long-lived remnant, a black-to-white-hole transition, or topology change. An answer is a classification derived in a UV-complete or otherwise controlled framework, giving the remnant mass and lifetime if any and the entropy carried by the final burst.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.evaporation-backreaction.remnant-consistency",
      "fields": {
        "precise": {
          "text": "Consider objects of mass $\\sim m_{P}$ with $N\\sim \\exp(S_{\\mathrm{initial}})$ internal states, where $S_{\\mathrm{initial}}$ can be arbitrarily large. Determine whether an effective field theory containing such remnants avoids pair-production rates and thermal contributions proportional to $N$, for example through form factors that suppress their couplings, while remaining unitary and local. Answer yes with a consistent model, or no with a general argument.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.problem-of-time.relational-equivalence",
      "fields": {
        "precise": {
          "text": "For a constrained quantum system with Hamiltonian constraint $H\\mid\\psi> = 0$, compare (i) the Page-Wootters conditional-state formalism, (ii) relational Dirac observables on the physical Hilbert space, and (iii) reduced quantization deparametrized with respect to a chosen clock. Determine conditions under which they give unitarily equivalent predictions, including clocks with degenerate or bounded spectra and clocks that interact with the rest of the system. An answer is an equivalence theorem with explicit conditions or a counterexample.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.strong-field-tests.echoes",
      "fields": {
        "precise": {
          "text": "For a nonspinning remnant of mass $M$ with a partially reflecting surface at areal radius $r_s+\\delta$, echoes repeat with delay Delta t ~ (4 G M/c^3) |ln(delta/r_s)|; a surface one Planck length $l_P=\\sqrt{G\\hbar/c^3}$, approximately $1.6 \\times 10^{-33}$ cm, of proper distance outside the horizon has $\\delta\\sim l_P^2/r_s$, so Delta t ~ (8 G M/c^3) ln(r_s/l_P). Determine whether data contain such echoes and bound the surface reflectivity $R$ as a function of the proper distance of the surface from the horizon, down to $l_P$. An answer is a detection or upper limits on R.",
          "how": [
            "outside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.strong-field-tests.kerr-spectroscopy-precision",
      "fields": {
        "status_note": {
          "text": "GW250114 gave two modes at $4.1\\,\\sigma$ with the overtone frequency consistent with Kerr to plus or minus $30\\%$ and the damping rate unconstrained (LIGO-Virgo-KAGRA 2025).",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.uv-completion.planck-lorentz-violation",
      "fields": {
        "status_note": {
          "text": "LHAASO observations of GRB 221009A give, for subluminal propagation, E_QG,1 > 10 E_P and E_QG,2 > $6 \\times 10^{-8}$ E_P at 95 percent confidence (2024); superluminal effects are bounded separately by the absence of photon decay.",
          "how": [
            "outside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "grav.uv-completion.which-completion",
      "fields": {
        "precise": {
          "text": "For a named candidate completion of $3+1$ gravity coupled to the Standard Model (string theory, asymptotic safety, loop quantum gravity, causal dynamical triangulations, Horava gravity or another), derive a low-energy observable, at energies far below $E_P=\\sqrt{\\hbar c^5/G}$, approximately $1.2 \\times 10^{19}$ GeV ($2 \\times 10^{16}$ erg), whose predicted deviation from general relativity plus the Standard Model is computed with stated uncertainty and is within reach of current or planned measurements. An answer is a falsifiable prediction with a stated magnitude that distinguishes the candidate from the alternatives.",
          "how": [
            "outside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.accelerator-dark-sectors.dark-photon",
      "fields": {
        "precise": {
          "text": "Determine whether a $U(1)'$ gauge boson $A'$ with mass $1\\,\\mathrm{MeV}$ to $10\\,\\mathrm{GeV}$ and kinetic mixing $\\epsilon \\sim 10^{-6}\\ \\text{to}\\ 10^{-3}$ exists, in visible ($A' \\to \\ell+ \\ell-$) or invisible decay modes. An answer is a resonance detection or exclusion of the remaining parameter space down to $\\epsilon \\sim 10^{-6}\\ \\text{to}\\ 10^{-5}$.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.accelerator-dark-sectors.higgs-invisible",
      "fields": {
        "precise": {
          "text": "Measure $\\operatorname{BR}(h \\to \\mathrm{invisible})$ beyond the SM $h \\to ZZ* \\to 4\\,\\nu$ value of $\\sim 1.2 \\times 10^{-3}$. LHC limits are about $0.1\\ \\text{to}\\ 0.15$ at 95 percent CL (ATLAS and CMS, 2023); an answer is a detection or a bound near $10^{-3}$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "HL-LHC vector-boson-fusion searches and a Higgs factory measuring Z h with $h \\to \\mathrm{invisible}$ to $\\sim 0.3\\%$.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.baryogenesis.baryon-asymmetry-origin",
      "fields": {
        "precise": {
          "text": "Explain $\\eta_B = n_B/n_\\gamma \\sim 6.1 \\times 10^{-10}$ (CMB and BBN) satisfying the Sakharov conditions, given that SM CP violation and the SM crossover fail by many orders of magnitude. An answer is a mechanism (thermal or resonant leptogenesis, electroweak baryogenesis, Affleck-Dine, or others) with an independent experimental confirmation.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.baryogenesis.ewbg-viability",
      "fields": {
        "precise": {
          "text": "Determine whether any model with a strongly first-order electroweak transition and CP violation sufficient for $\\eta_B \\sim 6 \\times 10^{-10}$ is consistent with $\\mid d_{e} \\mid <$ $4.1 \\times 10^{-30}$ e cm (JILA, 2023) and LHC Higgs data. An answer is an explicit viable model with predicted signals, or a general exclusion argument.",
          "how": [
            "inside:e-notation",
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "Next-generation electron EDM measurements (sensitivity $\\sim 10^{-31}\\,e\\,\\mathrm{cm}$) combined with Higgs self-coupling and singlet-mixing measurements.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.baryogenesis.low-scale-leptogenesis",
      "fields": {
        "precise": {
          "text": "Determine whether heavy neutral leptons N with $M_N \\sim 0.1\\ \\text{to}\\ 100\\ \\mathrm{GeV}$ and active-sterile mixing $U^2$ in the range where resonant or oscillation-based (ARS) leptogenesis gives $\\eta_B \\sim 6 \\times 10^{-10}$ exist. An answer is a discovery with measured $M_N$, $U_e^2$, $U_{\\mu}^2$, $U_{\\tau}^2$ consistent with that region, or its exclusion.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.dama-modulation.analysis-artifact",
      "fields": {
        "precise": {
          "text": "DAMA forms residuals by subtracting the annual mean rate per energy bin, cycle by cycle (roughly September to September). For a time-dependent background $B(t)$ (e.g., decaying cosmogenic or radiogenic components, or slow gain drift), this procedure induces a sawtooth residual whose fit to $A$ $\\mathrm{cos}(2 \\pi (t - t0)/1\\,\\mathrm{yr})$ can give a nonzero A with a phase that depends on $\\mathrm{d}B/\\mathrm{d}t$. An answer is a quantitative yes or no: whether a background evolution consistent with DAMA's published spectra and stability data reproduces the reported amplitude and phase.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.electroweak-anomalies.hvp-ee-tension",
      "fields": {
        "precise": {
          "text": "Identify the cause of the disagreement among $\\sigma(e+e- \\to \\pi+ \\pi-)$ measurements near the $\\rho$ peak (CMD-3 2023 versus KLOE, BaBar, SND) and between data-driven and lattice a_mu^HVP,LO (difference $\\sim 2\\ \\text{to}\\ 3\\%$ of HVP). An answer locates the systematic error, the radiative-correction issue, or a physical effect responsible.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.electroweak-anomalies.muon-g2-residual",
      "fields": {
        "precise": {
          "text": "Fermilab's final result (2025) gives $a_{\\mu} = 116592070.5(14.8) x 1e-11\\ (127\\ \\mathrm{ppb})$; the world average with BNL is $116592071.5(14.5) x 1e-11\\ (124\\ \\mathrm{ppb})$; the 2025 Theory Initiative prediction using lattice-QCD HVP (hadronic vacuum polarization) is $116592033(62) x 1e-11$, in agreement. The residual question is whether the SM prediction with uncertainty $\\sim 20 \\times 1e-11$ still agrees once data-driven and lattice HVP are reconciled.",
          "how": [
            "inside:x-times"
          ]
        },
        "settled_by": {
          "text": "Lattice HVP at $\\sim 0.2\\%$ from several groups, consistent $e+e-$ hadronic data, the MUonE spacelike HVP measurement, and the J-PARC muon $g-2$ experiment.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-anomalies.b-k-nunu",
      "fields": {
        "precise": {
          "text": "Belle II (2023) measured BR(B+ -> K+ nu nubar) = (2.3 +- 0.7) x $10^{-5}$, $2.7\\,\\sigma$ above the SM prediction ($\\sim 0.5 \\times 1e-5$). Determine whether the excess persists at $\\ge 5\\,\\sigma$ and whether it shows a peak in invisible mass from a new light particle.",
          "how": [
            "inside:x-times",
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-anomalies.b-s-mumu",
      "fields": {
        "precise": {
          "text": "Branching ratios of $B \\to K \\mu \\mu$ and $B_{s} \\to \\phi \\mu \\mu$ at low $q^{2}$ and the angular observable $P5'$ in $B \\to K* \\mu \\mu$ deviate from SM predictions by about $2 \\text{ to } 4 \\sigma$, while $R_{K}$ and $R_{K}*$ agree with the SM (LHCb, 2022). Identify whether a shift in the Wilson coefficient $C_{9}$ is short-distance new physics or long-distance c-cbar loops.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-anomalies.cabibbo-anomaly",
      "fields": {
        "precise": {
          "text": "Test $\\left|V_{ud}\\right|^2 + \\left|V_{us}\\right|^2 + \\left|V_{ub}\\right|^2 = 1$, with $V_{ud}$ from superallowed $0+$ to $0+$ nuclear beta decays and neutron decay, and $V_{us}$ from K_l3, K_mu2/pi_mu2 and $\\tau$ decays. The current deficit is of order $10^{-3}$ at about $3\\sigma$, together with an internal K_l3 versus K_mu2 tension; an answer is confirmation above $5\\sigma$ or resolution to below $2\\sigma$.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-anomalies.rd-rdstar",
      "fields": {
        "precise": {
          "text": "Determine whether $R(D)=\\operatorname{BR}(B \\to D \\tau \\nu)/\\operatorname{BR}(B \\to D \\ell \\nu)$ and $R(D*)$ exceed the SM values (HFLAV arithmetic average of predictions $0.296 \\pm 0.004\\ \\text{and}\\ 0.254 \\pm 0.005$). The HFLAV ICHEP 2026 averages are $R(D)=0.359 \\pm 0.024$ and $R(D*) = 0.280 \\pm 0.011$ (correlation -0.37), about $3.7\\,\\sigma$ above the SM combined; an answer is $\\ge 5\\,\\sigma$ confirmation or reduction below $2\\,\\sigma$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-puzzle.charged-lfv",
      "fields": {
        "title": {
          "text": "Does muon-to-electron conversion occur at rates near $10^{-16}$?",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Measure or bound the coherent conversion rate $R_{\\mathrm{mue}} = \\Gamma(\\mu- N \\to e- N)/\\Gamma(\\mu- \\mathrm{capture})$ on aluminum at single-event sensitivity $\\sim 10^{-17}$ (Mu2e, COMET), versus the SINDRUM II gold limit of about $7 \\times 10^{-13}$. Combine with $\\mu \\to e\\gamma$ (MEG II) and $\\mu \\to 3e$ (Mu3e) to identify the operator responsible if seen.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Mu2e at Fermilab and COMET at J-PARC reaching single-event sensitivity near $10^{-17}$.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "MEG II reported $\\mathrm{BR}(\\mu \\to e \\gamma) < \\sim 1.5 \\times 10^{-13}$ in 2025 (moderate confidence on the exact value); Mu2e and COMET are expected to start physics running around 2027.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.flavor-puzzle.yukawa-hierarchy",
      "fields": {
        "precise": {
          "text": "The SM Yukawa couplings span $y_e \\sim 3 \\times 10^{-6}$ to $y_t \\sim 1$, CKM angles are small ($\\theta_C \\sim 0.23$, $\\mid V_{ub}\\mid$ $\\sim 4 \\times 10^{-3}$) while PMNS angles are large ($\\theta_{12} \\sim 34\\,\\mathrm{deg}$, $\\theta_{23} \\sim 45\\,\\mathrm{deg}$). An answer is a mechanism (Froggatt-Nielsen charges, modular or discrete flavor symmetries, extra-dimensional localization, partial compositeness) that predicts these values with fewer parameters than it explains.",
          "how": [
            "inside:e-notation",
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.grand-unification.force-unification",
      "fields": {
        "plain": {
          "text": "The strengths of the three forces change with energy and nearly meet near $10^{16}\\, \\mathrm{GeV}$. Whether they truly become one force is unknown.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Determine whether SU(3) x SU(2) x U(1) embeds in a simple group ($\\mathrm{SU}(5), \\mathrm{SO}(10), \\mathrm{E6}$) broken near $M_{\\mathrm{GUT}} \\sim 10^{15}\\ \\text{to}\\ 10^{16}\\,\\mathrm{GeV}$. In the SM the three couplings do not meet at a point; in the MSSM they meet at $\\sim 2 \\times 10^{16}\\,\\mathrm{GeV}$. An answer is an observation of a unification-specific effect such as proton decay with a branching pattern fixed by the group.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.grand-unification.neutron-antineutron",
      "fields": {
        "precise": {
          "text": "Search for $\\Delta B = 2$ neutron-antineutron oscillations with free-neutron oscillation time $\\tau_{\\mathrm{nnbar}} > 8.6 \\times 10^{7}\\,\\mathrm{s}$ (ILL, 1994) and bound-neutron limits converting to $\\sim 4.7 \\times 10^{8}\\,\\mathrm{s}$ (Super-Kamiokande, 2021). An answer is a detection or a free-neutron limit improved by 1 to 3 orders of magnitude.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.grand-unification.p-nu-kaon",
      "fields": {
        "precise": {
          "text": "Measure or bound $\\tau(p \\to \\mathrm{anti}-\\nu K+)/B$, currently $> \\sim 5.9 \\times 10^{33}\\,\\mathrm{yr}$ (Super-Kamiokande, 2014). Minimal SUSY $\\mathrm{SU}(5)$ with dimension-5 operators predicts values near or below this; an answer is a detection or a limit $\\sim 10^{34}\\text{ to }10^{35}\\,\\mathrm{yr}$.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.grand-unification.proton-lifetime",
      "fields": {
        "title": {
          "text": "Is the proton lifetime to $e+ \\pi0$ below $10^{35}\\,\\mathrm{years}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "Measure or bound $\\tau(p \\to e+ \\pi0)/B$, currently $> 2.4 \\times 10^{34}\\,\\mathrm{yr}$ (Super-Kamiokande, 2020, 90 percent CL). Non-supersymmetric $\\mathrm{SO}(10)$ models with intermediate scales typically predict $10^{34}\\text{ to }10^{36}\\,\\mathrm{yr}$. An answer is a detection or a limit near $10^{35}\\,\\mathrm{yr}$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Hyper-Kamiokande exposure of about 1 to 2 Mt-yr reaching $\\sim 10^{35}\\,\\mathrm{yr}$ sensitivity.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.hierarchy-problem.neutral-naturalness",
      "fields": {
        "precise": {
          "text": "In neutral-naturalness models (Twin Higgs, folded supersymmetry, quirky little Higgs) the top-loop contribution to $m_h^{2}$ is cancelled by states without SM color, with a mirror-sector scale f; Higgs couplings shift by about $v^{2}/(2 f^{2})$ and the Higgs can decay to mirror glueballs with displaced vertices (approximate relations, model dependent). Determine whether such a sector exists with $f\\ \\text{below about}\\ 1\\ \\text{to}\\ 2\\ \\mathrm{TeV}$, by measuring $\\mathrm{BR}(h \\to \\text{mirror hadrons})$ down to about $10^{-4}$ and Higgs couplings at the per-mille level, or exclude it.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.hierarchy-problem.origin-weak-scale",
      "fields": {
        "plain": {
          "text": "The Higgs field sets the masses of most particles at about $246\\,\\mathrm{GeV}$, roughly $10^{17}$ times below the scale where gravity becomes strong. No known principle explains this huge gap without extreme fine cancellations.",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "In the SM with a cutoff $\\Lambda$, the top loop gives $\\delta m_h^{2} \\sim -(3 y_t^{2}/(8 \\pi^{2})) \\Lambda^{2}$, so $m_h = 125\\,\\mathrm{GeV}$ with $\\Lambda \\sim M_{\\mathrm{Pl}} \\sim 1.2 \\times 10^{19}\\,\\mathrm{GeV}$ requires cancellation to about 1 part in $10^{33}$. An answer is a mechanism (symmetry, compositeness, dynamics or selection) that yields $v = 246\\,\\mathrm{GeV}$ with at most mild tuning and is consistent with all LHC data.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.higgs-couplings.electron-yukawa",
      "fields": {
        "precise": {
          "text": "Measure the electron Yukawa coupling $y_e$ (SM value $\\sqrt{2}\\,m_e/v \\sim 2.9 \\times 10^{-6}$), or $\\kappa_e = y_e/y_e^{\\mathrm{SM}}$. The best direct bound, CMS $\\operatorname{BR}(H \\to e+ e-) < 3.0 \\times 10^{-4}$ at 95 percent CL (Phys. Lett. B 846, 137783, 2023), corresponds to $\\left|\\kappa_e\\right| < \\sim 240$ (approximate, using $\\operatorname{BR}_{\\mathrm{SM}} \\sim 5 \\times 10^{-9}$). An answer is $\\kappa_e$ measured with $O(1)$ precision, enough to separate $\\kappa_e = 1$ from $\\kappa_e = 0$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.higgs-couplings.second-generation",
      "fields": {
        "precise": {
          "text": "Measure the coupling modifiers $\\kappa_{\\mu}$ and $\\kappa_c$ relative to the SM. ATLAS Run 2 plus Run 3 $H \\to \\mu\\mu$ gives $3.4\\sigma$ ($2.5\\sigma$ expected) with signal strength $1.4 \\pm 0.4$ (Phys. Rev. Lett. 135, 231802, 2025), CMS Run 2 gives $3.0\\sigma$; the best direct charm bound is $\\left|\\kappa_c\\right| < 4.2$ at 95 percent CL (ATLAS VH, JHEP 04 (2025) 075). An answer is a $\\ge 5\\sigma$ observation of $H \\to \\mu\\mu$ with $\\kappa_{\\mu}$ to $\\sim 10\\%$, and a $\\kappa_c$ measurement that separates 1 from 0.",
          "how": [
            "inside:percent"
          ]
        },
        "settled_by": {
          "text": "HL-LHC $H \\to \\mu \\mu$ and $H \\to c\\ \\mathrm{cbar}$ analyses, followed by percent-level $\\mathrm{BR}(H \\to c\\ \\mathrm{cbar})$ and $\\operatorname{BR}(H \\to \\mu \\mu)$ measurements at a Higgs factory.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.higgs-couplings.total-width",
      "fields": {
        "precise": {
          "text": "Determine $\\Gamma_H$ with $\\le 5\\%$ uncertainty (SM: $4.1\\ \\mathrm{MeV}$). CMS used off-shell $H* \\to \\mathrm{ZZ}$ production to obtain $\\Gamma_H=3.2+2.4-1.7\\ \\mathrm{MeV}$ (Nature Physics 18, 1329, 2022), a method that assumes equal coupling modifiers on and off shell. An answer is a model-independent $\\Gamma_H$, which bounds the total rate of undetected and invisible decays.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.higgs-potential.trilinear-coupling",
      "fields": {
        "precise": {
          "text": "Measure $\\kappa_{\\lambda} = \\lambda_3/\\lambda_3^{\\mathrm{SM}}$, where the SM gives $\\lambda_3 = m_h^2/(2 v^2) \\sim 0.13$ for the cubic term $\\lambda_3 v h^3$. An answer is $\\kappa_{\\lambda}$ with total uncertainty below about 0.3 (30 percent), sufficient to distinguish the SM from models with a strongly first-order phase transition.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.higgs-potential.vacuum-metastability",
      "fields": {
        "settled_by": {
          "text": "A top-quark pole mass determination with uncertainty $\\sim 0.1\\,\\mathrm{GeV}$ (for example from a $t-\\mathrm{tbar}$ threshold scan at an $e+e-$ collider) together with $\\alpha_{s}(m_{Z})$ to $\\sim 0.1\\%$.",
          "how": [
            "inside:percent",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.low-energy-excess.calorimeter-mechanism",
      "fields": {
        "precise": {
          "text": "Cryogenic calorimeters (CRESST $\\mathrm{CaWO_4}$, $\\mathrm{Al_2O_3}$, Si; SuperCDMS-type Si and Ge; NUCLEUS; EDELWEISS) observe a rate $\\mathrm{d}R/\\mathrm{d}E$ rising steeply below about 200 eV, uncorrelated with particle backgrounds and decaying after cooldown. Candidate sources include stress relaxation at holders, glue and sensor films; dislocation motion from differential thermal contraction; and annealing of radiation-induced lattice defects. An answer is a mechanism that reproduces the energy spectrum, the time dependence, the material dependence and the sensor-geometry dependence, confirmed by a controlled test that turns the excess on or off.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-fog.8b-cevns-rate",
      "fields": {
        "precise": {
          "text": "Coherent elastic neutrino-nucleus scattering (CEvNS) of solar 8B neutrinos on Xe produces nuclear recoils below a few keV. The quantity is the measured 8B flux (or CEvNS rate) inferred from xenon data, compared with the SM cross section and the solar-model and SNO flux of about $5.2 \\times 10^{6}\\ \\mathrm{cm}^{-2}\\ \\mathrm{s}^{-1}$. An answer is a measurement with 10 percent precision and the resulting bound on nonstandard neutrino-quark couplings or light mediators.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-fog.directional-discrimination",
      "fields": {
        "precise": {
          "text": "In the neutrino fog, defined by O'Hare as the region where the discovery-limit index $n = -(d \\ln \\sigma / d \\ln \\mathrm{exposure})^{-1}$ exceeds 2, sensitivity grows slower than $1/\\sqrt{\\mathrm{exposure}}$. The question is the angular resolution, head-tail recognition efficiency and threshold (e.g., in a He:$\\mathrm{SF_6}$ or $\\mathrm{CF_4}$ gas time projection chamber) needed to restore n near 1 at WIMP masses 5-10 GeV and cross sections about one order of magnitude below the 8B fog boundary for the chosen target, and the exposure this requires.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-mass.absolute-mass",
      "fields": {
        "precise": {
          "text": "Determine $m_{\\mathrm{lightest}}$, or equivalently $m_{\\beta}=(\\sum\\left|U_{ei}\\right|^{2}m_i^{2})^{1/2}$ and $\\sum m_{\\nu}$. KATRIN (2025) gives $m_{\\beta}<0.45\\ \\mathrm{eV}$ (90 percent CL); oscillations require $\\sum m_{\\nu}\\ge \\sim 0.059\\ \\mathrm{eV}$ (normal) or $\\sim 0.10\\ \\mathrm{eV}$ (inverted). An answer is a nonzero value with $\\sim 20\\%$ uncertainty or a consistent upper limit across laboratory and cosmology.",
          "how": [
            "inside:operator-word",
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-mass.cp-phase",
      "fields": {
        "precise": {
          "text": "Measure the PMNS phase $\\delta_{\\mathrm{CP}}$ and determine whether $\\sin(\\delta_{\\mathrm{CP}}) \\ne 0$ at $\\ge 5\\sigma$ using $\\nu_{\\mu} \\to \\nu_e$ versus $\\mathrm{anti}-\\nu_{\\mu} \\to \\mathrm{anti}-\\nu_{e}$ appearance. Answer: $\\delta_{\\mathrm{CP}}$ with uncertainty $\\sim 10\\text{ to }20\\ \\mathrm{deg}$ and the yes-no CP verdict.",
          "how": [
            "inside:operator-word",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-mass.majorana-or-dirac",
      "fields": {
        "precise": {
          "text": "Determine whether lepton number is violated by Majorana neutrino masses via neutrinoless double beta decay, with half-life T_1/2 $\\sim 10^{26}$ to $10^{28}$ yr for $m_{bb} \\sim 10\\ \\text{to}\\ 50\\ \\mathrm{meV}$. KamLAND-Zen (2024) gives T_1/2(Xe-136) > $3.8 \\times 10^{26}$ yr, $m_{bb} < \\sim 28\\ \\text{to}\\ 122\\ \\mathrm{meV}$ (spread from nuclear matrix elements).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-mass.mass-ordering",
      "fields": {
        "precise": {
          "text": "Determine the sign of $\\Delta m^2_{31}$ ($\\left|\\Delta m^2_{31}\\right| \\sim 2.5 \\times 10^{-3}\\,\\mathrm{eV}^2$) at $\\ge 3\\,\\sigma$ from reactor oscillation spectra (JUNO), matter effects in long-baseline accelerator (DUNE, Hyper-K) and atmospheric data. Answer: normal or inverted.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.neutrino-mass.mass-origin",
      "fields": {
        "precise": {
          "text": "Identify the origin of $m_{\\nu} < \\sim 0.1\\ \\mathrm{eV}$: Dirac Yukawas with $y \\sim 10^{-12}$ plus right-handed neutrinos, the type I, II or III seesaw ($m_{\\nu} \\sim y^2 v^2 / M$), or radiative and low-scale mechanisms. An answer is the mechanism together with its scale, confirmed by a signature such as lepton number violation or heavy neutral leptons.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.sterile-neutrino-anomalies.ev-sterile",
      "fields": {
        "precise": {
          "text": "Determine whether a fourth mass state with $\\Delta m^2_{41} \\sim 0.1 \\text{ to } 10\\,\\mathrm{eV}^2$ and mixings |U_e4|, |U_mu4| large enough to produce sin^2(2 theta_mue) $\\sim 10^{-3}$ exists. An answer is a $5\\,\\sigma$ oscillation signal or exclusion of the region preferred by LSND and gallium in both appearance and disappearance.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.strong-cp.pq-quality",
      "fields": {
        "precise": {
          "text": "Planck-suppressed operators $O \\sim \\Phi^n / M_{\\mathrm{Pl}}^{(n-4)}$ shift $\\theta_{\\mathrm{bar}}$ by $\\sim f_a^n / (M_{\\mathrm{Pl}}^{(n-4)} m_a^2 f_a^2)$; keeping $\\mid\\theta_{\\mathrm{bar}}\\mid < 10^{-10}$ for $f_a \\sim 10^{10}\\,\\mathrm{GeV}$ requires $n > \\sim 10$. An answer is a UV mechanism (gauge discrete symmetries, composite or extra-dimensional axions) that provably forbids operators up to the required n with predicted low-energy signatures.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.strong-cp.qcd-axion-existence",
      "fields": {
        "precise": {
          "text": "Determine whether a pseudoscalar a with $m_a \\sim 5.7\\ \\mathrm{micro-eV}\\ (10^{12}\\ \\mathrm{GeV}/f_a)$ and photon coupling $g_{agamma}$ inside the QCD axion band (KSVZ to DFSZ and beyond) exists, for $f_a\\ \\text{between}\\ \\sim 10^{8}\\ \\text{and}\\ \\sim 10^{17}\\ \\mathrm{GeV}$. An answer is a detection with $m_a$ and $g_{agamma}$ consistent with the QCD mass-decay constant relation, or exclusion of the band over the full range.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.strong-cp.theta-smallness",
      "fields": {
        "title": {
          "text": "Why is the QCD $\\theta$ angle smaller than $10^{-10}$?",
          "how": [
            "inside:e-notation"
          ]
        },
        "plain": {
          "text": "The strong-force angle $\\theta$ could have any value up to about 3, yet the neutron's electric dipole moment shows it is below $10^{-10}$. No reason for this is known.",
          "how": [
            "inside:e-notation"
          ]
        },
        "precise": {
          "text": "The physical parameter $\\theta_{\\mathrm{bar}} = \\theta - \\arg \\det(M_{q})$ induces $d_{n} \\sim 10^{-16}\\ \\theta_{\\mathrm{bar}}\\ e\\ \\mathrm{cm}$; the PSI bound $\\mid d_{n}\\mid < 1.8 \\times 10^{-26}\\ e\\ \\mathrm{cm}$ (90 percent CL, 2020) gives $\\mid\\theta_{\\mathrm{bar}}\\mid < \\sim 10^{-10}$. An answer is a mechanism (Peccei-Quinn axion, massless up quark, spontaneous CP or P violation such as Nelson-Barr) consistent with lattice QCD and flavor data.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.sub-gev-detection.daily-modulation-anisotropy",
      "fields": {
        "precise": {
          "text": "For sub-GeV dark matter scattering via phonons or electrons in anisotropic crystals (e.g., $\\mathrm{Al_2O_3}$, hexagonal BN, graphene-like or Dirac materials), the rate $R(t)$ modulates with sidereal period because the dark matter wind direction rotates relative to the crystal axes; predicted fractional amplitudes reach tens of percent in some materials. The question is whether a modulation of this size can be measured at sub-eV thresholds with exposure below about $1\\,\\mathrm{kg}\\,\\mathrm{yr}$, given present low-energy excess rates, and whether the excess itself shows any sidereal modulation.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.sub-gev-detection.freeze-in-reach",
      "fields": {
        "precise": {
          "text": "In the freeze-in benchmark with an ultralight dark-photon mediator, the DM-electron cross section $\\sigma_e(m_{\\chi})$ is fixed by the relic abundance. For $m_{\\chi}$ below about 1 MeV the kinetic energy $(1/2) m_{\\chi} v^2$ with $v \\sim 10^{-3} c$ is below the 1.1 eV silicon gap, so semiconductor targets lose sensitivity. The question is whether a target with meV-scale gap or collective response (superconductors, Dirac materials, polar crystals via in-medium dark-photon mixing, superconducting nanowires) reaches the freeze-in line for $m_{\\chi} = 10\\,\\mathrm{keV} - 1\\,\\mathrm{MeV}$, accounting for in-medium screening.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "hep.sub-gev-detection.single-phonon-calorimetry",
      "fields": {
        "precise": {
          "text": "Dark matter of mass $m_{\\chi} \\sim 10\\,\\mathrm{keV} - 10\\,\\mathrm{MeV}$ scattering via a dark-photon or hadrophilic mediator excites single optical or acoustic phonons of energy $\\omega \\sim 10-100\\,\\mathrm{meV}$ in polar crystals (GaAs, $\\mathrm{Al_2O_3}$, $\\mathrm{SiO_2}$). The question is whether a phonon sensor (transition-edge sensor, kinetic-inductance detector, superconducting qubit) can reach an energy threshold below 100 meV with dark-count rate below about 1 event/(kg day) at that threshold. An answer is a demonstrated threshold and background, or a proof-of-limit from sensor noise and phonon down-conversion losses.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.anderson-delocalization.2d-localization",
      "fields": {
        "precise": {
          "text": "For $H = \\Delta + \\lambda V$ on $\\ell^2(Z^2)$, $\\Delta$ the nearest-neighbour hopping operator (spectrum $[-4, 4]$ at $\\lambda = 0$), $V$ i.i.d. with bounded density (or Bernoulli), prove that for every $\\lambda > 0$ the spectrum is almost surely pure point with exponentially decaying eigenfunctions at all energies, with localization length expected to grow as $\\exp(c/\\lambda^2)$. Answer: a proof.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.anderson-delocalization.band-matrices",
      "fields": {
        "precise": {
          "text": "Hermitian random band matrices on the box $\\{1..L\\}^{d}$ with variance profile of width $W$. Prove for $d = 3$ that bulk eigenvectors are delocalized for $W \\ge W_0$ fixed and $L \\to \\infty$, and for $d = 2$ that the localization length scales as $\\exp(c W^2)$. Answer: proofs of these scalings.",
          "how": [
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "Proofs of delocalization for fixed large $W$ in $d = 3$ and of the $\\exp(c W^{2})$ localization length in $d = 2$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.anderson-delocalization.quantum-diffusion",
      "fields": {
        "precise": {
          "text": "For $H = \\Delta + \\lambda V$ on $Z^3$, $\\Delta$ the nearest-neighbour hopping operator, show that $E \\sum_{x} \\mid x \\mid^{2} \\mid \\langle x \\mid \\mathrm{exp}(-itH) \\mid 0\\rangle \\mid^{2} \\sim D(\\lambda) t$ as $t \\to \\infty$ with a diffusion constant $D(\\lambda) > 0$ for small $\\lambda$ (or the analogous statement for an energy-localized initial state). Erdos, Salmhofer and Yau proved diffusion up to times $t \\sim \\lambda^{-2-\\kappa}$ for some $\\kappa > 0$. Answer: a proof for $t \\to \\infty$ at fixed small $\\lambda$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.bose-condensation.bec-thermo-limit",
      "fields": {
        "precise": {
          "text": "$N$ bosons in a box of side $L$ in $R^{3}$, $H = \\sum_i -\\operatorname{Lap}_i + \\sum_{i<j} v(x_i - x_j)$ with $v \\ge 0$ compactly supported, density $\\rho = N/L^{3}$ fixed, $L \\to \\infty$. Prove at $T = 0$ or at small $T > 0$ that the one-body density matrix has off-diagonal long-range order, lim_{|x-y| -> infinity} gamma^(1)(x,y) = $\\rho$_0 > 0. Answer: a proof for some open range of rho and $T$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.bose-condensation.hardcore-off-half-filling",
      "fields": {
        "precise": {
          "text": "Hard-core bosons on $Z^3$, H = -sum_<xy> (a_x^+ a_y + a_y^+ a_x), equivalently the spin-$1/2$ XY model in a uniform field along z, at density $\\rho \\text{ in } (0,1), \\rho != 1/2$. Prove off-diagonal long-range order, $\\lim_{\\mid x-y\\mid \\to \\infty} \\langle a_x^{+} a_y\\rangle > 0$, for $T$ below some $T_c(\\rho) > 0$. Answer: a proof for an open interval of $\\rho$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.bose-condensation.third-order-energy",
      "fields": {
        "precise": {
          "text": "With $\\hbar^{2}/(2m) = 1$, the ground-state energy density is predicted to be $e(\\rho) = 4 \\pi a \\rho^2 [1 + (128/(15 \\sqrt{\\pi})) (\\rho a^3)^{1/2} + 8 (4 \\pi/3 - \\sqrt{3}) \\rho a^3 \\log(\\rho a^3) + o(\\rho a^3 \\log(\\rho a^3))]$ (Wu, 1959). Prove the matching lower bound for general short-range $v \\ge 0$. Answer: a proof of the two-sided expansion.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.crystallization.cohn-kumar-2d",
      "fields": {
        "precise": {
          "text": "Prove that for every density $\\rho$ the triangular lattice minimizes the energy per point $\\sum_{y != x} f(\\mid x - y \\mid^{2})$ among all periodic configurations in $R^{2}$ of density $\\rho$, for every completely monotone f (including $\\exp(-a r^{2})$ and $r^{-s}$). Answer: proof or a periodic configuration beating the triangular lattice for some such f.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.crystallization.sticky-spheres-3d",
      "fields": {
        "precise": {
          "text": "For $V(r)=+\\infty \\text{ for } r<1, -1 \\text{ for } r=1, 0 \\text{ for } r>1 \\text{ in } R^3$, minimizing $E_N$ is maximizing the contact number $c(N)$ of $N$ non-overlapping unit-diameter spheres. Prove that for large N every minimizer coincides, except for $o(N)$ spheres, with a subset of a close packing (a stacking of triangular layers), and determine whether $\\lim(6N-c(N))/N^{2/3}$ exists and, if so, its value (expected to be set by the surface energy of the optimal close-packed shape).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.fluid-singularities.axisymmetric-swirl-ns",
      "fields": {
        "precise": {
          "text": "3D Navier-Stokes on $R^{3}$ with $f = 0$ and smooth, finite-energy, axisymmetric initial data with nonzero swirl $u_{\\theta}$. Prove global regularity, or give smooth axisymmetric data whose solution has $\\operatorname{limsup}_{t \\to T} \\mid\\mid u(t)\\mid\\mid_{\\infty} = \\infty$. Answer: yes or no with proof; this is a special case of mathph.fluid-singularities.ns-unforced.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.fluid-singularities.euler-smooth-r3",
      "fields": {
        "precise": {
          "text": "Incompressible Euler on $R^3$ (or $T^3$): does there exist smooth finite-energy initial data (e.g. $C_c^{\\infty}$) whose solution satisfies $\\int_0^T \\mid\\mid \\omega(t)\\mid\\mid_{\\operatorname{inf}} dt = \\infty$ at a finite $T$, with $\\omega = \\operatorname{curl} u$ (Beale-Kato-Majda criterion)? Known: blowup for smooth data in a cylinder with boundary (Chen and Hou, computer-assisted, PNAS 2025) and for $C^{(1,\\alpha)}$ data on $R^3$ (Elgindi, Annals of Mathematics 2021, small $\\alpha$; Cordoba, Martinez-Zoroa and Zheng, Annals of PDE 2025). Answer: a verified construction or a proof of global regularity.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.fluid-singularities.leray-hopf-uniqueness",
      "fields": {
        "precise": {
          "text": "3D Navier-Stokes on $R^{3}$ with $f = 0$ and divergence-free $u_{0}$ in $L^{2}$: is the Leray-Hopf weak solution ($u\\ \\text{in}\\ L^{\\infty}_{t} L^{2}_{x}$ and $L^{2}_{t} H^{1}_{x}$, satisfying the energy inequality) unique? Albritton, Brue and Colombo proved non-uniqueness for a force $f\\ \\text{in}\\ L^{1}_{t} L^{2}_{x}$ built from an unstable self-similar profile. Answer: yes or no with proof.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.fluid-singularities.ns-unforced",
      "fields": {
        "precise": {
          "text": "Incompressible Navier-Stokes $\\mathrm{d}u/\\mathrm{d}t + (u.\\mathrm{grad})u = \\nu\\,\\mathrm{Lap}\\,u - \\mathrm{grad}\\,p, \\mathrm{div}\\,u = 0$, on $R^3$ or the torus $T^3$ with $\\nu > 0$, external force $f = 0$ and smooth divergence-free initial data (Schwartz class on $R^3$). Answer: a proof that the smooth solution exists for all $t > 0$ (Clay statements A and B), or smooth data whose solution has $\\operatorname{limsup}_{t \\to T} \\mid\\mid u(t)\\mid\\mid_{\\infty} = \\infty$ at a finite $T$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.fluid-singularities.sqg-blowup",
      "fields": {
        "precise": {
          "text": "Inviscid SQG: $\\mathrm{d}\\theta/\\mathrm{d}t + u . \\mathrm{grad}\\,\\theta = 0$, $u = (-R_2 \\theta, R_1 \\theta)$ with $R_j$ the Riesz transforms, on $R^2$ or $T^2$, smooth (e.g. $C_c^\\infty$) initial $\\theta$, no forcing. Prove global regularity, or give smooth data with $\\int_{0}^{T} ||\\mathrm{grad}\\,\\theta(t)||_{\\mathrm{inf}}\\,\\mathrm{d}t = \\infty$ at finite T. Answer: yes or no with proof.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.ionization.atomic-radius",
      "fields": {
        "plain": {
          "text": "Heavy atoms are about the same size as light ones, roughly $10^{-8}$ cm across. Prove from the many-electron Schrodinger equation that the size of a neutral atom does not grow with Z.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.ionization.molecular-excess",
      "fields": {
        "precise": {
          "text": "For $K$ static nuclei with charges $Z_1, ..., Z_K$ at positions $R_1, ..., R_K$, $Z_{\\mathrm{tot}} = \\sum_k Z_k$, and $N$ electrons with Coulomb interactions, let $N_c$ be the largest N for which the electronic ground state is bound. Prove $N_c \\le Z_{\\mathrm{tot}} + C K$ with C independent of the $Z_{k}$, $R_{k}$ and K, or give a counterexample family.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.ising-rigorous.exponents-exist",
      "fields": {
        "precise": {
          "text": "Nearest-neighbour Ising model on $Z^3$ at $\\beta_c$. Prove that $\\langle s_0 s_x\\rangle_{\\beta_c}=\\left|x\\right|^{-(1+\\eta)+o(1)}$ and that the correlation length $\\xi(\\beta)=(\\beta_c-\\beta)^{-\\nu+o(1)}$, with numerical values $\\eta\\ \\mathrm{approximately}\\ 0.0363$ and $\\nu\\ \\mathrm{approximately}\\ 0.6300$. Answer: a proof of existence of the limits, with or without their values.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.ising-rigorous.ising-4d-logs",
      "fields": {
        "settled_by": {
          "text": "A proof of the $\\mid\\log\\mid^{1/3}$ susceptibility correction for the nearest-neighbour 4D Ising model.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.kam-stability.diffusion-time",
      "fields": {
        "settled_by": {
          "text": "A construction of diffusing orbits with time $\\exp(C \\epsilon^{-1/(2n)})$ for an open set of perturbations.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.kam-stability.elliptic-equilibrium-instability",
      "fields": {
        "precise": {
          "text": "Real-analytic $H$ on $R^{2n}$, $n \\ge 3$, with $H = \\sum_i \\omega_i (p_i^2 + q_i^2)/2 + O(3)$, $\\omega$ non-resonant and not all $\\omega_i$ of one sign. Prove that the origin is Lyapunov unstable for generic higher-order terms (open dense or residual set in a suitable analytic topology). Answer: a proof, or a stable open set of examples.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.kam-stability.generic-arnold-diffusion",
      "fields": {
        "precise": {
          "text": "$H = h(I) + \\varepsilon f(\\theta, I)$, $(\\theta, I)\\ \\mathrm{in}\\ T^{n} x R^{n}$, h strictly convex, $n \\ge 3$. Prove that for generic f (residual in $C^r$, r large; separately, for an open set of analytic f) and all small $\\varepsilon > 0$ there are orbits with $\\mid I(T) - I(0) \\mid \\ge c$ with c independent of $\\varepsilon$. Answer: a proof for every $n \\ge 3$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.lieb-thirring-constants.clr-constant",
      "fields": {
        "precise": {
          "text": "For $-\\Delta + V$ on $L^2(R^3)$, the Cwikel-Lieb-Rozenblum bound reads $N(V) \\le L_{0,3} \\int V_-^{(3/2)} dx$, $N(V)$ = number of negative eigenvalues. Determine the sharp $L_{0,3}$; it exceeds $L^{\\mathrm{cl}}_{0,3} = 1/(6 \\pi^2)$, and it is unknown whether it equals the one-bound-state value $L^1_{0,3}$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.lieb-thirring-constants.critical-exponent",
      "fields": {
        "precise": {
          "text": "Define $\\gamma_c(d) = \\mathrm{inf}\\{\\gamma : L_{\\gamma,d} = L^{\\mathrm{cl}}_{\\gamma,d}\\}$, where $L^{\\mathrm{cl}}_{\\gamma,d} = \\Gamma(\\gamma+1)/((4 \\pi)^{d/2} \\Gamma(\\gamma+1+d/2))$; $L_{\\gamma,d}/L^{\\mathrm{cl}}_{\\gamma,d}$ is nonincreasing in $\\gamma$ (Aizenman, Lieb 1978). Known: $1 \\le \\gamma_c(d) \\le 3/2$ for all d (lower bound Helffer, Robert 1990; upper bound Laptev, Weidl, Acta Math 2000), $\\gamma_c(1) = 3/2$, and $\\gamma_c(2)$ $\\ge\\ \\mathrm{about}\\ 1.165$, the exponent at which the one-bound-state and semiclassical constants cross. Determine $\\gamma_c(2)$ and $\\gamma_c(3)$; the 1976 conjecture $\\gamma_c(3) = 1$ follows from a proof of mathph.lieb-thirring-constants.kinetic-3d.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.lieb-thirring-constants.kinetic-3d",
      "fields": {
        "precise": {
          "text": "For $-\\Delta + V$ on $L^2(R^3)$ (units $\\hbar^2/(2m) = 1$) with negative eigenvalues $E_j$, prove or disprove $\\sum_j \\mid E_j \\mid \\le L^{\\mathrm{cl}}_{1,3} \\int V_-^{5/2}\\, dx$ with $L^{\\mathrm{cl}}_{1,3} = 1/(15 \\pi^2)$. Dual form: for orthonormal $\\phi_1..\\phi_N$ in $L^2(R^3)$, $\\sum_j \\int \\mid \\mathrm{grad}\\, \\phi_j \\mid^2 \\ge (3/5)(6 \\pi^2)^{2/3} \\int \\rho^{5/3}$, $\\rho = \\sum_j \\mid \\phi_j \\mid^2$. Answer: a proof, or a potential with ratio greater than 1.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.lieb-thirring-constants.one-dim-intermediate",
      "fields": {
        "precise": {
          "text": "For $-\\mathrm{d}^2/\\mathrm{d}x^2 + V$ on $L^2(R)$, with $L_{\\gamma,1}$ the sharp constant in $\\sum_j \\left|E_j\\right|^\\gamma \\le L_{\\gamma,1} \\int V_-^{(\\gamma + 1/2)} dx$, prove $L_{\\gamma,1} = L^1_{\\gamma,1}$ for $1/2 < \\gamma < 3/2$, where $L^1_{\\gamma,1}$ is the sharp constant over potentials with exactly one negative eigenvalue. Known endpoints: equality at $\\gamma = 1/2$ (Hundertmark, Lieb, Thomas 1998) and $L_{\\gamma,1} = L^{\\mathrm{cl}}_{\\gamma,1}$ for $\\gamma \\ge 3/2$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.quantum-chaos.hilbert-polya",
      "fields": {
        "precise": {
          "text": "Find a self-adjoint operator $H$ on a Hilbert space, defined independently of the zeros, with spectrum $\\{\\gamma_n\\}$ where $\\zeta(1/2 + i \\gamma_n) = 0$, and prove the spectral identity. The Berry-Keating proposal $H = xp$ with suitable boundary conditions reproduces the smooth counting function $N(E) \\sim (E/(2 \\pi)) \\log(E/(2 \\pi e)) + 7/8$ but not the individual zeros. Answer: an explicit operator with proof.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.quantum-chaos.montgomery-pair",
      "fields": {
        "precise": {
          "text": "Let $F(\\alpha)$ be Montgomery's pair correlation function of normalized zeros. Prove $F(\\alpha) = 1$ for $\\mid\\alpha\\mid \\ge 1$ (assuming RH), which gives the GUE pair correlation $1 - (\\sin(\\pi u)/(\\pi u))^2$ for all test functions; it is proven only for Fourier support in $\\mid\\alpha\\mid < 1$. Answer: a proof.",
          "how": [
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "A proof of $F(\\alpha) = 1$ for $\\mid \\alpha \\mid \\ge 1$, or of the pair correlation for test functions with Fourier support beyond $[-1, 1]$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.quantum-chaos.random-wave-model",
      "fields": {
        "settled_by": {
          "text": "A proof of Gaussian moments (e.g. $||\\phi_j||_4^4 \\to 3/\\mathrm{vol}(M)$) for a density-one subsequence on one negatively curved surface.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.quantum-spin-gaps.haldane-spin1",
      "fields": {
        "precise": {
          "text": "$H = \\sum_i S_i . S_{i+1}$ with $S = 1$ on a ring of L sites. Prove $\\mathrm{inf}_{L} (E_{1}(L) - E_{0}(L)) > 0$ (numerically the gap is approximately $0.4105 J$), together with a unique infinite-volume ground state with exponentially decaying correlations. Answer: a proof.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.sigma-models.correlation-length-asymptotics",
      "fields": {
        "precise": {
          "text": "For the $O(N)$ model on $Z^2$ with $N \\ge 3$, prove $\\xi(\\beta) = C_N \\beta^{-1/(N-2)} \\exp(2 \\pi \\beta/(N-2)) (1 + o(1))$ as $\\beta \\to \\infty$, with $\\xi = 1/m$ the exponential correlation length; the constant $C_N$ was predicted by Hasenfratz, Maggiore and Niedermayer (1990) from the Bethe ansatz. Answer: a proof of the leading asymptotics, with or without the constant.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.sigma-models.polyakov-mass-gap",
      "fields": {
        "precise": {
          "text": "Classical $O(N)$ model on $Z^{2}$, $N \\ge 3$, spins $s_{x}$ in $S^{N-1}$, Gibbs weight exp(beta sum_<xy> s_x . s_y). Prove that for every $\\beta < \\infty$ there are $C, m(\\beta) > 0$ with $\\langle s_{0} . s_{x}\\rangle \\le C\\ \\exp(-m(\\beta)\\ \\mid x\\mid)$ uniformly in the volume. For $N = 2$ the opposite holds at large $\\beta$ (power-law decay, Frohlich and Spencer, 1981). Answer: a proof, or a proof of a massless low-temperature phase.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.yang-mills.continuum-limit-4d",
      "fields": {
        "precise": {
          "text": "Take $\\mathrm{SU}(N)$ lattice gauge theory with the Wilson action on $(\\epsilon \\mathrm{Z})^4$, with bare coupling chosen by asymptotic freedom, $g(\\epsilon)^2 \\sim 1/(2 b_0 \\log(1/(\\epsilon \\Lambda)))$ with $b_0 = 11 N/(48 \\pi^2)$, i.e. $1/g^2 \\sim (11 N/(24 \\pi^2)) \\log(1/(\\epsilon \\Lambda))$. Prove that correlations of gauge-invariant observables (smoothed Wilson loops or smeared $F^2$) converge as $\\epsilon \\to 0$ in infinite volume to a non-Gaussian limit satisfying the Osterwalder-Schrader axioms. Answer: a proof.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "mathph.yang-mills.mass-gap",
      "fields": {
        "precise": {
          "text": "For every compact simple gauge group $G$ ($SU(2)$ is the minimal case), construct a quantum Yang-Mills theory on $R^4$ satisfying the Osterwalder-Schrader or Wightman axioms, and prove a mass gap: the Hamiltonian $H$ has spectrum contained in $\\{0\\}\\cup[\\Delta, \\infty)$ for some $\\Delta > 0$. Answer: a proof of both statements (Jaffe-Witten formulation for the Clay Mathematics Institute).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.bnct.accelerator-source",
      "fields": {
        "precise": {
          "text": "Design an accelerator-driven source giving epithermal neutron flux above $10^9\\,\\mathrm{per}\\,\\mathrm{cm}^2\\,\\mathrm{per}\\,\\mathrm{s}$ at the beam port with fast-neutron and photon dose per epithermal neutron below the IAEA-recommended limits (of order $2 \\times 10^{-11}$ $\\mathrm{rad}\\ \\mathrm{cm}^{2}$ each), using $\\mathrm{Li}-7(p,n)$, $\\mathrm{Be}-9(p,n)$ or $(d,n)$ reactions, with target lifetime of at least hundreds of treatment hours under proton-induced blistering and heat loads of order $10^{11}\\,\\mathrm{erg}/\\mathrm{s}$. An answer is a source with measured spectrum, flux and target lifetime meeting all criteria.",
          "how": [
            "outside:x-times",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.bnct.mixed-field-weighting",
      "fields": {
        "precise": {
          "text": "Construct a model converting the absorbed dose components of a neutron capture field (B-10(n,$\\alpha$)Li-7 at about 2.3 MeV total kinetic energy, N-14(n,p) protons at 0.58 MeV, fast-neutron recoil protons and photons) into a photon-isoeffective dose that predicts tumour control and normal-tissue complication, replacing fixed compound and relative biological effectiveness factors. The model must include the boron microdistribution relative to the nucleus and dose-rate effects over treatment times of 30 to 60 min. An answer is a validated weighting scheme with stated uncertainty.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.diffusion-mri.time-dependence-class",
      "fields": {
        "precise": {
          "text": "For the diffusion coefficient $D(t)$ in tissue approaching its long-time value as $D(t) - D_{\\infty} \\sim t^{-\\theta}$, with $\\theta = (p + d)/2$ where d is the spatial dimension of the relevant disorder and p the structural exponent of its density correlations at long wavelengths, measure $\\theta$ and assign p for white matter along and across axons, grey matter and muscle. An answer is a classification of tissues by p with measured exponents and uncertainty.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.dosimetry.ion-beam-quality",
      "fields": {
        "precise": {
          "text": "Reduce the uncertainty in the mean energy per ion pair in air $W_{\\mathrm{air}}$ and in the beam-quality correction factor $k_Q$ for carbon and other ions to the level needed for a total dosimetric uncertainty below $1.5\\%$. ICRU 90 values are $W_{\\mathrm{air}}$ of about $34.44\\,\\mathrm{eV}$ for protons (about $0.4\\%$ standard uncertainty) and $34.71\\,\\mathrm{eV}$ for carbon ions (about $1.5\\%$). An answer is a measured value set with reduced uncertainty.",
          "how": [
            "inside:percent"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.flash.human-sparing",
      "fields": {
        "title": {
          "text": "Does the FLASH sparing effect occur in human normal tissue?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.flash.oxygen-depletion",
      "fields": {
        "title": {
          "text": "Can radiolytic oxygen depletion quantitatively explain FLASH sparing?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.focused-ultrasound.histotripsy-predictability",
      "fields": {
        "precise": {
          "text": "Predict the threshold and spatial extent of histotripsy bubble-cloud formation from the incident pressure waveform, with peak negative pressures of $10^8\\text{ to }3 \\times 10^8\\,\\mathrm{dyn}/\\mathrm{cm}^2$ and microsecond pulses, including nucleus distribution in tissue, shock scattering from earlier bubbles, and tissue mechanical properties. An answer is a predictive model giving the treated volume boundary to within $1\\,\\mathrm{mm}$.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.ion-therapy.optimal-ion",
      "fields": {
        "title": {
          "text": "Which ion species is optimal for therapy?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.low-dose-risk.linearity",
      "fields": {
        "title": {
          "text": "Does risk stay linear below 10 rad?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.microdosimetry.predictive-observable",
      "fields": {
        "title": {
          "text": "Which nanoscale observable predicts biological effect?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.pcct.k-edge-sensitivity",
      "fields": {
        "precise": {
          "text": "Determine the minimum detectable concentration of K-edge elements (iodine at 33.2 keV, gadolinium at 50.2 keV, and higher-$Z$ labels such as tantalum, gold and bismuth) in a 30 cm diameter water phantom at clinical dose, as a function of detector energy resolution, bin count and photon flux. An answer is a detection-limit formula in mg per cm^3 with its dependence on these quantities.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.pet.timing-limit",
      "fields": {
        "title": {
          "text": "Is 10 ps coincidence time resolution reachable?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "med.radionuclide-therapy.dose-response",
      "fields": {
        "title": {
          "text": "Does absorbed dose predict outcome in radionuclide therapy?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Establish whether tumour absorbed dose, computed from quantitative imaging and time-activity integration for Lu-177 labelled agents, predicts response with a slope distinguishable from zero, and whether kidney and marrow absorbed dose predicts toxicity. Typical delivered tumour doses span $10^3$ to $3 \\times 10^4\\,\\mathrm{rad}$ at dose rates of 1 to 100 rad/h. An answer is a dose-response relation with confidence intervals, or a demonstration that dose rate and biological factors dominate.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.ab-initio-nuclei.lead-neutron-skin",
      "fields": {
        "precise": {
          "text": "PREX-II gives $R_{\\mathrm{skin}}(208\\mathrm{Pb})$ = $R_{n} - R_{p}$ = $0.283 \\pm 0.071\\ \\mathrm{fm}$ and CREX gives $R_{\\mathrm{skin}}(48\\mathrm{Ca})$ = $0.121 \\pm 0.026\\ (\\mathrm{exp}) \\pm 0.024\\ (\\mathrm{model})\\ \\mathrm{fm}$. Determine whether a single nuclear Hamiltonian or energy density functional reproduces both measured parity-violating asymmetries $A_{\\mathrm{PV}}$, and fix $R_{\\mathrm{skin}}(208\\mathrm{Pb})$ to $\\pm 0.03\\ \\mathrm{fm}$. Answer: a consistent description, or the identified experimental or theoretical cause of the tension.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.ab-initio-nuclei.spectroscopic-factor-quenching",
      "fields": {
        "precise": {
          "text": "Define $R_s = \\sigma_{\\exp}/\\sigma_{\\mathrm{th}}$, the ratio of measured to predicted (shell model times reaction theory) single-nucleon removal cross sections, and $\\Delta S$, the separation energy of the removed nucleon minus that of the other species. Intermediate-energy knockout on light targets shows $R_s$ falling from roughly 0.9 to roughly 0.3 as $\\Delta S$ goes from about $-20$ to $+20\\,\\mathrm{MeV}$, whereas transfer, $(p, 2p)$, $(p, pn)$ and $(e, e' p)$ data show weak or no dependence (Aumann et al., Prog. Part. Nucl. Phys. 118, 103847, 2021). Answer: whether the trend reflects nuclear correlations or reaction-model approximations (eikonal and sudden treatment, core excitation), with an ab initio prediction of $R_s(\\Delta S)$ consistent across reaction types.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.double-beta-nme.double-gamow-teller-correlation",
      "fields": {
        "precise": {
          "text": "Shell-model calculations show a near-linear correlation between the ground-state double Gamow-Teller matrix element $M^{\\mathrm{DGT}}$ and $M^{0\\nu}$ (Shimizu, Menendez and Yako, PRL 120, 142502, 2018). Determine whether the correlation holds across many-body methods and with two-body currents, and extract $M^{\\mathrm{DGT}}$ from heavy-ion double-charge-exchange reactions (NUMEN at LNS Catania, RCNP Osaka). Answer: yes or no for model independence, with calibration slope and uncertainty.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.emc-src.tagged-dis-virtuality",
      "fields": {
        "precise": {
          "text": "Measure the struck-nucleon structure function in $d(e, e' N_s) X$ as a function of $x'$ and spectator momentum $p_s$ from $0.25\\text{ to }0.6\\ \\mathrm{GeV}/c$ (JLab BAND and LAD experiments), and determine whether $F2_{\\mathrm{bound}}/F2_{\\mathrm{free}}$ scales with the virtuality $v = (p^\\mu p_\\mu - M^2)/M^2$ as SRC models predict. Answer: the measured function $F2_{\\mathrm{bound}}/F2_{\\mathrm{free}}(x', v)$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.exotic-hadrons.pc-spin-parity",
      "fields": {
        "precise": {
          "text": "$\\mathrm{Pc}(4440)+$ and $\\mathrm{Pc}(4457)+$ appear in $J/\\psi\\,p$ from $\\Lambda_{b} \\to J/\\psi\\,p\\,K-$ (LHCb, PRL 122, 222001, 2019), about 20 and 3 MeV below the $\\Sigma_{c}+ \\mathrm{anti}-D*0$ threshold. Determine $J^{P}$ of each from a full amplitude analysis. Answer: $J^{P}$ values; the $\\Sigma_{c}\\ \\mathrm{anti}-D*$ molecular picture predicts $1/2-$ and $3/2-$, with the ordering set by short-range contact terms.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.exotic-hadrons.x3872-compositeness",
      "fields": {
        "plain": {
          "text": "The chi_c1(3872), also called $X(3872)$, lies within about 0.2 MeV of the combined mass of two charmed mesons, $D0$ and $\\mathrm{anti}-D*0$. Measuring its exact position and line shape decides how much of it is a loose two-meson molecule.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "A direct energy scan in antiproton-proton annihilation (PANDA at FAIR) or high-statistics $D0\\ \\mathrm{anti}-D0\\ \\pi0$ line shapes at LHCb or Belle II.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.fission-theory.spin-opening-angle",
      "fields": {
        "precise": {
          "text": "Compute and measure the distribution $P(\\cos\\theta_{\\mathrm{LH}})$ of the opening angle between the fragment spin vectors $J_{\\mathrm{L}}$ and $J_{\\mathrm{H}}$ in $252\\mathrm{Cf}(\\mathrm{sf})$ or $235\\mathrm{U}(n_{\\mathrm{th}},\\mathrm{f})$. Bending modes favor antiparallel spins and wriggling modes favor parallel spins perpendicular to the fission axis, while statistical post-scission generation gives a nearly isotropic distribution; the answer is the measured distribution and which mode content it implies.",
          "how": [
            "inside:operator-word"
          ]
        },
        "status_note": {
          "text": "Time-dependent density-functional and statistical (FREYA) predictions of $P(\\cos \\theta_{\\mathrm{LH}})$ differ, with a 2024 analysis tracing part of the difference to quantal spin effects; no measurement of the opening-angle distribution was found as of 2026.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.gluon-saturation.coherent-vector-meson",
      "fields": {
        "precise": {
          "text": "In ultraperipheral $\\mathrm{Pb}+\\mathrm{Pb}$ collisions at $\\sqrt{s_{NN}} = 5.02\\,\\mathrm{TeV}$, CMS and ALICE extracted the coherent $J/\\psi$ photonuclear cross section down to $x \\sim 10^{-5}$ using forward-neutron tagging and found a suppression relative to the impulse approximation that persists or flattens at the smallest $x$. Determine whether leading-twist nuclear shadowing, saturation in a dipole picture with nonlinear evolution, or another mechanism quantitatively accounts for the W_gammaN dependence and the $\\mid t \\mid$ spectrum.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "The 2023 CMS and ALICE neutron-tagged measurements removed the ambiguity over which nucleus emitted the photon, and no model describes the full $x$ dependence down to $x \\sim 10^{-5}$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.gluon-saturation.saturation-existence",
      "fields": {
        "precise": {
          "text": "Establish whether the growth of the gluon distribution $x\\,g(x, Q^2)$ in protons and heavy nuclei at $x < 10^{-3}$ and $Q^2$ of a few $\\mathrm{GeV}^2$ is modified by nonlinear recombination, as described by the Balitsky-Kovchegov and JIMWLK evolution equations, with a saturation scale $Q_s^2(x) \\sim A^{1/3} x^{-\\lambda}, \\lambda \\sim 0.3$. A yes requires an observable whose measured A and x dependence is reproduced by nonlinear evolution and excluded, at high significance, by linear DGLAP evolution with fitted nuclear parton distributions.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.gluon-saturation.saturation-scale-nuclei",
      "fields": {
        "precise": {
          "text": "Determine $Q_s^{2}(x)$ for Au and Pb at $x=10^{-3}\\ \\text{and}\\ 10^{-4}$ with uncertainty below 30 percent, including the actual A dependence (versus the naive $A^{1/3}$ scaling) and the impact-parameter profile. Estimates of order $1\\ \\text{to}\\ 2\\ \\mathrm{GeV}^{2}$ at $x\\sim 10^{-3}$ depend on the dipole model and the definition of $Q_s$; the answer must state the definition and the data used.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.neutrino-nucleus.pion-production",
      "fields": {
        "plain": {
          "text": "In the few-GeV range many neutrino collisions make a pion, often through a short-lived excited nucleon called the $\\Delta$. Measurements from different experiments and the models used to describe them do not agree, especially for slow pions and small momentum transfers.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.neutron-star-matter.hyperon-puzzle",
      "fields": {
        "settled_by": {
          "text": "Femtoscopic $\\Lambda-\\mathrm{p}$ and $\\Lambda-\\mathrm{d}$ correlation data from the LHC and RHIC and hypernuclear spectroscopy that fix the $\\Lambda-\\mathrm{NN}$ force, combined with quantum Monte Carlo calculations of hyperonic matter.",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Repulsive $\\Lambda-\\mathrm{NN}$ forces fitted to hypernuclei can suppress hyperons (Lonardoni et al., 2015), but the three-body force remained poorly constrained as of 2026.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.neutron-star-matter.pressure-density-relation",
      "fields": {
        "status_note": {
          "text": "Combined analyses since 2018 constrain the radius of a 1.4 solar-mass star to roughly $1.15 \\times 10^{6}$ to $1.3 \\times 10^{6}$ cm, while the pressure above about $3 n_{0}$ remained weakly constrained as of 2026.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.precision-anomalies.lambda-correlation-tension",
      "fields": {
        "precise": {
          "text": "PERKEO III, from the $\\beta$ asymmetry $A$, gives $\\lambda = -1.27641(45)(33)$ (Markisch et al., PRL 122, 242501, 2019); aSPECT, from the electron-antineutrino correlation $a = -0.10430(84)$, gives $\\mid \\lambda \\mid = 1.2677(28)$ (Beck et al., PRC 101, 055506, 2020). Determine whether the difference is an experimental systematic or a sign of scalar or tensor couplings that shift A, a and the Fierz term $b$ differently. Answer: a consistent $\\lambda$ from $A, a \\text{ and } \\tau_{n}$ with uncertainty below $3 \\times 10^{-4}$, or a nonzero exotic coupling.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.precision-anomalies.superallowed-nuclear-corrections",
      "fields": {
        "title": {
          "text": "Nuclear-structure corrections in superallowed $\\beta$ decays",
          "how": [
            "ai:gpt-5.5"
          ]
        },
        "precise": {
          "text": "Compute the isospin-symmetry-breaking correction $\\delta_{C}$ and the nuclear-structure-dependent radiative correction $\\delta_{\\mathrm{NS}}$ for the best-measured superallowed 0+ -> 0+ transitions (10C to 74Rb) with absolute uncertainty below $10^{-4}$, using ab initio methods with electroweak currents. Answer: corrected Ft values and $V_{ud}$, deciding whether the first-row CKM sum $\\mid V_{ud}\\mid^{2}+\\mid V_{us}\\mid^{2}+\\mid V_{ub}\\mid^{2}$ deviates from 1 (reported deficit of about 2 to 3 standard deviations).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.precision-anomalies.x17-anomaly-origin",
      "fields": {
        "status_note": {
          "text": "MEG II (2024) found no signal in $7\\mathrm{Li}(p, e+ e-)8\\mathrm{Be}$ and set 90 percent CL limits $R < 1.8 \\times 10^{-6}$ ($17.6\\,\\mathrm{MeV}$) and $R < 1.2 \\times 10^{-5}$ ($18.1\\,\\mathrm{MeV}$) on the X17 branching ratio relative to gamma emission, while PADME (2025) reported an excess near $16.90\\,\\mathrm{MeV}$ with a global significance of about 2 standard deviations.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.precision-anomalies.x17-boson-search",
      "fields": {
        "precise": {
          "text": "Test for a vector or axial-vector boson with $m_X = 16.5 \\text{ to } 17.2\\,\\mathrm{MeV}$ and electron coupling $\\epsilon$ of roughly $2 \\times 10^{-4} \\text{ to } 1.4 \\times 10^{-3}$ through resonant $e+ e- \\to X \\to e+ e-$ production (PADME), electron beam-dump and pair-spectrometer experiments. Answer: discovery, or exclusion at 90 percent confidence of the full coupling range implied by the ATOMKI 8Be and 4He rates.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.proton-structure.charge-radius-residual",
      "fields": {
        "plain": {
          "text": "Muonic hydrogen (a proton orbited by a muon, a heavy cousin of the electron) and the most precise hydrogen measurements give a proton radius of about $0.84\\,\\mathrm{fm}$ ($1\\,\\mathrm{fm} = 10^{-13}\\,\\mathrm{cm}$). Electron-scattering experiments disagree with each other, one giving $0.83\\,\\mathrm{fm}$ and an older one $0.88\\,\\mathrm{fm}$, and the cause is not identified.",
          "how": [
            "inside:e-notation"
          ]
        },
        "settled_by": {
          "text": "Low-momentum-transfer $\\mathrm{e}-\\mathrm{p}$ and $\\mu-\\mathrm{p}$ scattering (PRad-II, MUSE, AMBER) analyzed with a common radiative-correction and fitting treatment, together with an independent reanalysis of the Mainz A1 data.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.proton-structure.gluon-helicity",
      "fields": {
        "precise": {
          "text": "Determine $\\Delta G(\\mu^{2})=\\int_{0}^{1}\\mathrm{d}x\\ \\Delta g(x,\\mu^{2})$ at $\\mu^{2}=10\\ \\mathrm{GeV}^{2}$, where $\\Delta g$ is the gluon helicity distribution and x the gluon momentum fraction. RHIC polarized pp data give $\\int_{0.05}^{0.2}\\Delta g\\ \\mathrm{d}x=0.20\\ (+0.06,-0.07)$ (de Florian et al., 2014) under a positivity assumption; the open part is $x<0.01$, where no data exist, together with the residual dependence of the sign on high-x and $\\mathrm{SU}(3)$ assumptions. Answer: $\\Delta G$ with total uncertainty below 0.05.",
          "how": [
            "inside:operator-word"
          ]
        },
        "settled_by": {
          "text": "Scaling violations of the polarized structure function $g_{1}$ measured at the EIC over $10^{-4} < x < 0.5$, combined in a global fit with RHIC data.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.proton-structure.orbital-angular-momentum",
      "fields": {
        "precise": {
          "text": "Extract the quark orbital angular momentum $L_q = J_q - \\Delta \\Sigma_q/2$ with $J_q = (1/2)\\,\\int dx\\, x\\, [H_q(x,0,0) + E_q(x,0,0)]$, where $H$ and $E$ are generalized parton distributions (GPDs, functions encoding both momentum and transverse position of partons) measured in deeply virtual Compton scattering and exclusive meson production, together with the gluon $J_g$. Answer: $L_u, L_d\\ \\text{and}\\ J_g$ at $\\mu^2 = 4\\,\\mathrm{GeV}^2$ with uncertainties below 0.05, satisfying the spin sum rule.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.proton-structure.spin-decomposition",
      "fields": {
        "settled_by": {
          "text": "Polarized electron-proton collisions at the EIC (Electron-Ion Collider, Brookhaven) covering x down to about $10^{-4}$, combined with lattice QCD calculations of quark and gluon angular momenta at physical quark masses.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.qcd-phase-diagram.critical-point",
      "fields": {
        "precise": {
          "text": "Determine whether the chiral crossover line $T_{\\mathrm{pc}}(\\mu_B)$ ($T_{\\mathrm{pc}}(0)$ about $156\\,\\mathrm{MeV}$, $\\mu_B$ the baryon chemical potential) ends at a critical point $(T_c, \\mu_B,c)$ beyond which the transition is first order, and locate it. Lattice QCD disfavors a critical point at $\\mu_B/T$ below about 3. Answer: yes or no, and $(T_c, \\mu_B,c)$ with uncertainty.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.quark-gluon-plasma.early-hydrodynamization",
      "fields": {
        "plain": {
          "text": "Fluid models describe heavy-ion collisions starting about $3 \\times 10^{-24}$ seconds after impact, which seems too early for the matter to have settled down. How the system starts behaving as a fluid so soon is not fully understood.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.quark-gluon-plasma.phi-spin-alignment",
      "fields": {
        "plain": {
          "text": "In off-center heavy-ion collisions the produced matter rotates, and spinning particles should line up slightly with the rotation. STAR found that $\\phi$ mesons (strange quark plus strange antiquark) line up far more than expected, while $K*0$ mesons do not.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.r-process-nuclear.neutron-capture-rates",
      "fields": {
        "precise": {
          "text": "Determine $(n, \\gamma)$ rates at $T\\ \\text{about}\\ 10^{9}\\,\\mathrm{K}$ for nuclei 10 to 20 neutrons beyond stability to within a factor of 2 (model predictions differ by up to two orders of magnitude far from stability), using indirect methods: the beta-Oslo method (gamma strength and level density from beta-decay feeding), surrogate reactions, and $(d, p)$ on radioactive beams. Answer: rates for the nuclei with largest abundance sensitivity and validated statistical-model inputs.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.stellar-reaction-rates.c12-alpha-gamma",
      "fields": {
        "precise": {
          "text": "Determine the total astrophysical S-factor $S_{\\mathrm{tot}}(E_{\\mathrm{cm}}=300\\,\\mathrm{keV})$ of $\\mathrm{12C}(\\alpha,\\gamma)\\mathrm{16O}$ (E1 and E2 ground-state transitions plus cascades), at the Gamow peak for $T \\sim 2 \\times 10^{8}\\,\\mathrm{K}$, with total uncertainty below 10 percent. Direct data stop near $E_{\\mathrm{cm}} \\sim 1\\,\\mathrm{MeV}$, so the answer requires either direct data closer to 300 keV or an R-matrix extrapolation whose subthreshold-state inputs (1- at 7.12 MeV and 2+ at 6.92 MeV in 16O) are fixed to the needed accuracy.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.stellar-reaction-rates.c12c12-resonances",
      "fields": {
        "precise": {
          "text": "Determine the total $\\mathrm{12C}+\\mathrm{12C}$ fusion $S*$-factor (alpha plus proton channels) for $E_{\\mathrm{cm}}=1.5\\ \\text{to}\\ 2.5\\,\\mathrm{MeV}$, the Gamow window for $T=5 \\times 10^{8}\\ \\text{to}\\ 10^{9}\\,\\mathrm{K}$, including the presence, energies and strengths of any resonances, and hence the reaction rate at $T=5 \\times 10^{8}\\ \\text{to}\\ 10^{9}\\,\\mathrm{K}$ to 20 percent. The answer must reconcile direct particle-gamma coincidence data, which extend down to about $E_{\\mathrm{cm}} \\sim 2.2\\,\\mathrm{MeV}$, with indirect Trojan-horse extractions that claim strong resonant enhancement below 2 MeV.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.stellar-reaction-rates.electron-screening-excess",
      "fields": {
        "precise": {
          "text": "Low-energy measurements of $3\\mathrm{He}(d,p)4\\mathrm{He}$, $6,7\\mathrm{Li}(p,\\alpha)$ and $d(d,p)t$ yield screening potentials $U_e$, defined by $\\sigma_{\\mathrm{screened}}(E)/\\sigma_{\\mathrm{bare}}(E)\\sim \\exp(\\pi \\eta U_e/E)$ with $\\eta$ the Sommerfeld parameter, that exceed the adiabatic limit $U_{\\mathrm{ad}}$ (the difference in electron binding between the separated atoms and the united atom) by up to a factor $\\sim 2$ in gas targets and by an order of magnitude for deuterons in some metal hosts. Explain the excess quantitatively, and determine whether the error lies in the screening physics, in stopping-power corrections, or in the extrapolated bare S-factors.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.stellar-reaction-rates.i-process-sites",
      "fields": {
        "precise": {
          "text": "The i-process operates at neutron densities $n_n \\sim 10^{13} \\text{ to } 10^{16}\\,\\mathrm{cm}^{-3}$, between the s-process ($\\sim 10^{7} \\text{ to } 10^{10}\\,\\mathrm{cm}^{-3}$) and the r-process ($> 10^{20}\\,\\mathrm{cm}^{-3}$), and is invoked for carbon-enhanced metal-poor stars with mixed s and r signatures, Sakurai's object and some presolar grains. Identify which candidate sites (proton ingestion into helium-flash convective zones of low-metallicity AGB and super-AGB stars, rapidly accreting white dwarfs, helium shells of massive stars) produce the observed $[\\mathrm{Ba}/\\mathrm{La}]$, $[\\mathrm{La}/\\mathrm{Eu}]$ and $[\\mathrm{Ba}/\\mathrm{Eu}]$ ratios, and with what neutron exposure, given the large uncertainties in neutron-capture rates on unstable nuclei near $A \\sim 130 \\text{ to } 140$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "nuc.stellar-reaction-rates.p-nuclei-mo-ru",
      "fields": {
        "precise": {
          "text": "92Mo, 94Mo, 96Ru and 98Ru make up roughly 15, 9, 5.5 and 1.9 percent of solar Mo and Ru, while gamma-process yields (photodisintegration of seed nuclei at $T \\sim 2 \\times 10^{9}\\ \\text{to}\\ 3 \\times 10^{9}\\ \\mathrm{K}$) in core-collapse supernovae and standard Type Ia models underproduce them by an order of magnitude or more relative to other p-nuclei. Identify the site or combination of sites (neutrino-driven proton-rich outflows, the nu p-process; Type Ia explosions of s-process-enriched white dwarfs; oxygen-carbon shell mergers in massive stars) that reproduces their solar abundances and the 92Mo/94Mo ratio with realistic nuclear rates.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.burning-plasma.alpha-turbulence",
      "fields": {
        "title": {
          "text": "Do $\\alpha$ particles reduce or increase turbulent heat loss?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.burning-plasma.helium-ash",
      "fields": {
        "title": {
          "text": "Can helium ash be exhausted fast enough in a reactor?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.collisionless-shocks.electron-injection",
      "fields": {
        "precise": {
          "text": "Diffusive shock acceleration (DSA, repeated shock crossings by particles scattered by magnetic turbulence) requires electron gyroradii larger than the shock width (of order the ion inertial length). Determine the injection efficiency and the electron-to-proton ratio $K_{\\mathrm{ep}}$ at equal energy as functions of Alfvenic Mach number $M_A$, sonic Mach number and shock obliquity $\\theta_{Bn}$ at realistic $m_i/m_e$. An answer is $K_{\\mathrm{ep}}(M_A, \\theta_{Bn})$ from converged kinetic simulations, compared with $K_{\\mathrm{ep}} \\sim 10^{-3}\\ \\text{to}\\ 10^{-2}$ inferred in supernova remnants.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.collisionless-shocks.field-amplification-saturation",
      "fields": {
        "plain": {
          "text": "Cosmic rays streaming ahead of a shock can amplify the magnetic field, which helps trap particles and accelerate them to higher energy. How strong the amplified field becomes, which decides whether supernova remnants can accelerate protons to about $10^{15}$ electron volts, is unsettled.",
          "how": [
            "outside:e-notation"
          ]
        },
        "precise": {
          "text": "Cosmic-ray-current-driven instabilities (notably the nonresonant Bell instability) amplify the upstream field of fast shocks. Determine the saturated amplitude $deltaB/B_{0}$ and its coherence length as functions of shock speed $v_{\\mathrm{sh}}$ and cosmic-ray acceleration efficiency, including the saturation mechanism (expansion of current-driven cavities, back-reaction on the cosmic rays, nonlinear damping). An answer is $deltaB/B_{0}(v_{sh}, efficiency)$ from kinetic or hybrid simulations converged over many growth times, with an analytic saturation model from which the maximum proton energy at young supernova remnants follows.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.collisionless-shocks.weibel-field-survival",
      "fields": {
        "precise": {
          "text": "In relativistic unmagnetized or weakly magnetized ($\\sigma$ below about $10^{-3}$) electron-positron and electron-ion shocks, the Weibel (current-filamentation) instability generates fields with energy fraction $\\epsilon_B\\sim0.01\\ \\text{to}\\ 0.1$ near the shock, which decay within about $10^{2}$ to $10^{3}$ skin depths $c/\\omega_p$ in particle-in-cell simulations. Determine whether self-consistent particle acceleration and upstream precursor fields sustain $\\epsilon_B$ of $10^{-5}$ to $10^{-2}$ over distances many orders of magnitude larger, as afterglow modeling infers, and give $\\epsilon_B$ versus distance downstream. An answer is a derived decay law validated by long particle-in-cell runs.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.disruptions.benign-termination",
      "fields": {
        "precise": {
          "text": "In JET, DIII-D and TCV, low-$Z$ ($\\mathrm{D_2}$) injection into a runaway plateau purges high-$Z$ impurities, lowers resistivity and triggers a large MHD instability that deposits the beam energy over a wide wetted area with little avalanche regeneration. Determine whether this benign termination survives at ITER beam current and energy, where regeneration and the instability's wetted area differ. An answer is yes or no for the ITER reference runaway plateau, with the predicted peak wall energy deposition.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.disruptions.predictor-transfer",
      "fields": {
        "title": {
          "text": "Can a disruption predictor trained elsewhere protect a new tokamak?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.disruptions.runaway-current-iter",
      "fields": {
        "precise": {
          "text": "In ITER disruptions mitigated by shattered pellet injection (SPI, fragmented $\\mathrm{D_2}$ and Ne pellets), a small runaway seed from hot-tail generation, tritium beta decay and Compton scattering of gamma rays from the activated wall is amplified by avalanche multiplication. Compute the final runaway current versus injected D and Ne quantities, including losses through stochastic magnetic fields during the thermal quench and runaway-driven kinetic instabilities, and determine whether any injection scheme keeps the runaway current below the wall-tolerable level.",
          "how": [
            "outside:chemical"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.disruptions.thermal-quench",
      "fields": {
        "precise": {
          "text": "Identify what sets the thermal quench duration (about $10^{-3}$ s or less in large tokamaks): magnetic stochastization by global MHD modes, radiative collapse, and parallel heat transport in stochastic fields. Predict the quench time, the radiated versus conducted energy fraction and the wall heat-load distribution for ITER. An answer is 3D nonlinear MHD with validated kinetic heat-flux closures reproducing measured quench times across devices.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.edge-pedestal-elms.elm-energy-loss",
      "fields": {
        "title": {
          "text": "What sets the energy lost per ELM at low collisionality?",
          "how": [
            "title:question-mark"
          ]
        },
        "settled_by": {
          "text": "Nonlinear MHD simulations that reproduce the measured $\\Delta W_{ELM}(\\nu*_{ped})$ trend and heat-load footprints on two devices, applied to ITER without retuning.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.edge-pedestal-elms.elm-free-reactor-regime",
      "fields": {
        "title": {
          "text": "Is any ELM-free or small-ELM regime compatible with reactor conditions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.edge-pedestal-elms.rmp-elm-iter",
      "fields": {
        "title": {
          "text": "Will resonant magnetic perturbations suppress ELMs in ITER?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.exb-low-temperature.anomalous-mobility-closure",
      "fields": {
        "precise": {
          "text": "In Hall thrusters (radial $B$ of order 100 to 300 G, xenon propellant), the measured cross-field electron mobility exceeds the classical collisional value by one to three orders of magnitude and varies along the channel. Derive a closure $\\mu_{\\mathrm{perp}}(z)$ from local plasma parameters that, inserted in fluid or hybrid codes, predicts thrust, discharge current and breathing-mode oscillations to within 10 percent without tuning, across thrusters and operating points.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.hed-fusion.direct-drive-lpi",
      "fields": {
        "precise": {
          "text": "At ignition-scale direct drive (intensity about $10^{22}\\,\\mathrm{erg}\\,\\mathrm{s}^{-1}\\,\\mathrm{cm}^{-2}$), cross-beam energy transfer, two-plasmon decay and stimulated Raman scattering reduce absorption and produce hot electrons that preheat the fuel. Determine the absorbed fraction and the hot-electron preheat energy at full scale, and whether broadband or multi-color laser light suppresses them enough to allow $G$ above 10. An answer is a validated kinetic plus hydrodynamic prediction tested at intermediate scale.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.hed-fusion.maglif-high-gain",
      "fields": {
        "title": {
          "text": "Can magnetized liner inertial fusion reach high gain?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "In magnetized liner inertial fusion (MagLIF: axial seed field of order $10^{5}\\ \\mathrm{G}$, laser-preheated D or DT fuel, liner imploded by a current pulse of about $20\\ \\mathrm{MA}$ on the Z machine), magnetic insulation lowers the required fuel areal density. Determine whether integrated designs reach ignition and gain $G\\ \\text{above}\\ 10$ at drive currents of $40\\ \\text{to}\\ 70\\ \\mathrm{MA}$, given measured limits from magneto-Rayleigh-Taylor growth, preheat-induced mix and magnetized electron heat transport (Nernst advection). An answer is a radiation-MHD design validated on Z data at $20\\ \\mathrm{MA}$, or a demonstrated scaling showing it fails.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.hed-fusion.target-gain-ten",
      "fields": {
        "title": {
          "text": "Can laser-driven inertial fusion reach target gain of 10?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Target gain $G$ $= \\text{fusion yield}/\\text{laser energy}$ on target exceeded 1 at the National Ignition Facility in December 2022 with about $2.05 \\times 10^{13}$ erg of laser energy. Determine whether $G$ of at least 10 is reachable at laser energy of about $2 \\times 10^{13}$ to $3 \\times 10^{13}$ erg by any design (indirect drive, direct drive, shock ignition, magnetized targets) given measured limits from hydrodynamic instabilities, ablator-fuel mix and drive asymmetry. An answer is an experiment, or a radiation-hydrodynamics design validated against existing ignition shots.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "NIF reached target gain 4.13 on 7 April 2025 ($8.6 \\times 10^{13}$ erg yield from $2.08 \\times 10^{13}$ erg of laser energy) and about 3.8 in June 2026; gain 10 has not been reached.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.kinetic-turbulence-dynamo.dissipation-mechanism",
      "fields": {
        "title": {
          "text": "Which mechanisms dissipate turbulence in the solar wind?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.kinetic-turbulence-dynamo.helicity-barrier",
      "fields": {
        "title": {
          "text": "Does the helicity barrier control ion heating in imbalanced solar wind?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.qed-cascades.intensity-limit",
      "fields": {
        "title": {
          "text": "Does pair cascade absorption cap the attainable laser intensity?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Fedotov, Narozhny, Mourou and Korn (2010) argued that cascades seeded by a single pair deplete the laser field and limit the attainable focused field to far below $E_{S} \\sim 4.4 \\times 10^{13}\\ \\mathrm{statvolt/cm}$. Determine the maximal attainable peak field in a vacuum focus as a function of input power ($10\\text{-}100\\ \\mathrm{PW}$, multi-beam dipole focusing), including seeding by residual gas, by target debris and by pairs created from vacuum, and decide whether ultrahigh vacuum, pulse shaping or tight focusing lifts the limit.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.qed-cascades.lab-avalanche-threshold",
      "fields": {
        "precise": {
          "text": "In counterpropagating or multi-beam (dipole-wave) laser fields an avalanche cascade, with pair number growing as $\\exp(\\Gamma t)$ over several laser periods, is predicted above an intensity of order $10^{31}\\ \\mathrm{erg}\\ \\mathrm{s}^{-1}\\ \\mathrm{cm}^{-2}$ for 1-micron light, about ten times the record peak intensity of about $10^{30}\\ \\mathrm{erg}\\ \\mathrm{s}^{-1}\\ \\mathrm{cm}^{-2}$ (2021, approximate). Determine the minimal laser energy and geometry (colliding pulses, dipole focusing, single-pulse reflection from a plasma mirror) at which the pair number grows by several e-foldings, and observe it through positron yield scaling that exceeds the one-generation shower prediction.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.qed-cascades.pulsar-multiplicity",
      "fields": {
        "title": {
          "text": "Can pulsar pair cascades supply the pairs inferred in pulsar wind nebulae?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Polar-cap cascade models give a maximum pair multiplicity $\\kappa = n_{\\mathrm{pairs}}/n_{\\mathrm{GJ}}$ of a few times $10^{5}$ (Timokhin and Harding 2019), where $n_{\\mathrm{GJ}}$ is the Goldreich-Julian charge density, reached for the strongest fields and hottest surfaces in their model grid. Spectral models of the Crab nebula infer $\\kappa$ of order $10^{6}$ or more (moderate confidence). Determine whether polar-cap, outer-gap and current-sheet pair production together supply the nebular pair content inferred from radio to gamma-ray spectra, or whether the nebular inference must be revised.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.radiation-reaction.classical-limit-equation",
      "fields": {
        "title": {
          "text": "Which classical radiation-reaction equation is the classical limit of QED?",
          "how": [
            "title:owner"
          ]
        },
        "precise": {
          "text": "The Lorentz-Abraham-Dirac (LAD) equation, third order in time with characteristic time $\\tau_0 = 2 e^2/(3 m c^3) \\sim 6.3 \\times 10^{-24}\\,\\mathrm{s}$, has runaway and preaccelerating solutions; restricting LAD to its non-runaway (critical) manifold gives a second-order equation whose first-order approximation in $\\tau_0$ is the Landau-Lifshitz (LL) equation; the two differ from order $\\tau_0^2$ on. Determine the classical limit ($\\hbar \\to 0$ at fixed classical field parameters) of QED for a point charge in a background field to all orders in $\\tau_0$, and identify whether it coincides with LL, with LAD on the critical manifold, or with another second-order equation (for example Ford-O'Connell), at orders beyond the leading one in $\\alpha$.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.radiation-reaction.stochastic-emission-signature",
      "fields": {
        "precise": {
          "text": "For $\\chi \\sim 0.1-1$ the quantum-stochastic description predicts electron energy straggling (growth of energy spread) and quantum quenching, both absent in quantum-continuous models (LL with a Gaunt-factor reduction of the emitted power). In head-on electron-laser collisions with $a0 \\sim 10-100$ and $\\gamma \\sim 10^{3}-10^{4}$, measure post-collision electron spectra (energy spread evolution, high-energy tail) or photon spectra with precision sufficient to reject the quantum-continuous model at $5\\,\\sigma$, controlling shot-to-shot jitter in collision timing and overlap.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.reconnection.coronal-sheet-onset",
      "fields": {
        "precise": {
          "text": "For a current sheet of length $L$ and thickness a forming under external driving in resistive or Hall MHD at Lundquist number $S = L v_A/\\eta$ of $10^{12}$ to $10^{14}$ (solar corona), determine the aspect ratio $a/L$ and the time at which tearing growth outpaces sheet thinning and fast (plasmoid-mediated or collisionless) reconnection begins; the ideal-tearing proposal gives $a/L \\sim S^{-1/3}$. Determine how the criterion depends on the thinning rate and on the approach to kinetic scales ($a \\sim d_i$), and predict the stored magnetic energy at onset. An answer is a criterion confirmed by driven-sheet simulations over a range of $S$ and consistent with flare-onset observations.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.reconnection.nonthermal-spectrum",
      "fields": {
        "precise": {
          "text": "For relativistic pair-plasma or electron-ion reconnection with magnetization $\\sigma = B^2/(4 \\pi w)$ ($w$ = relativistic enthalpy density) from 1 to $10^{3}$, determine the index $p$ of $dN/dgamma \\sim \\gamma^{-p}$ and the high-energy cutoff $\\gamma_{\\max}$ as functions of $\\sigma$, guide field and system size $L/d_e$ in 3D, in the limit $L/d_e$ going to infinity. An answer is $p(\\sigma, B_g)$ and the scaling of $\\gamma_{\\max}$ with $L$, converged in system size.",
          "how": [
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        },
        "settled_by": {
          "text": "3D particle-in-cell simulations converged in system size, with an analytic acceleration model reproducing $p\\ \\text{and}\\ \\gamma_{\\max}$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.reconnection.plasmoid-regime-3d",
      "fields": {
        "precise": {
          "text": "In resistive (and Hall) MHD reconnection with Lundquist number $S = L v_{A}/\\eta$ far above the critical $S_{c} \\sim 10^{4}$, $2\\mathrm{D}$ simulations give a rate $\\sim 0.01 v_{A} B_{0}/c$ independent of $S$ and a power-law plasmoid size distribution. Determine in $3\\mathrm{D}$ the asymptotic rate as $S$ goes to $\\infty$, the critical $S_c$, the flux-rope size distribution and whether self-generated turbulence makes the $3\\mathrm{D}$ rate differ from the 2D value. An answer is converged $3\\mathrm{D}$ values with error bars.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.reconnection.sawtooth-incomplete-reconnection",
      "fields": {
        "precise": {
          "text": "Kadomtsev full reconnection predicts that the central safety factor $q_0$ rises to 1 after each crash on a time $\\sim (\\tau_A\\tau_R)^{1/2}$ ($\\tau_A$ Alfven time, $\\tau_R$ resistive time), while motional-Stark-effect and Faraday-rotation measurements find $q_0$ remaining near 0.7 to 0.8 and crash times of order $10^{-4}\\,\\mathrm{s}$ in large hot tokamaks. Identify the mechanism (two-fluid fast reconnection, island stochastization, pressure-driven secondary instability, stabilization by fast ions or diamagnetic effects) that sets the crash time, the post-crash $q$ profile and the complete versus incomplete outcome. An answer is a model predicting these three quantities across devices.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.sfqed-breakdown.finite-pulse-relevance",
      "fields": {
        "title": {
          "text": "Does the Ritus-Narozhny scaling survive in realistic finite-duration fields?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "The $(\\alpha \\chi^{2/3})^n$ loop scaling (Ritus-Narozhny conjecture) holds in an infinite constant crossed field; for finite plane-wave pulses at fixed intensity parameter $a0 = e E/(m c \\omega)$ and growing particle energy, loop corrections to observables grow only logarithmically (Podszus and Di Piazza 2019; Ilderton 2019), with the constant-field behavior recovered only under a condition of the form $\\chi$ $<< a0^{3}$ (approximate). Determine the region in the space of $a0, \\chi$ and pulse phase duration in which n-loop corrections to physical observables (photon emission probability, pair yield, electron mass shift) scale as $(\\alpha \\chi^{2/3})^n$, and decide whether that region overlaps $\\alpha \\chi^{2/3} >\\sim 1$ for any physically realizable background, including non-plane-wave fields such as colliding beams.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.sfqed-breakdown.physics-beyond",
      "fields": {
        "title": {
          "text": "What theory describes QED at $\\alpha \\chi^{2/3}$ much larger than one?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.sfqed-breakdown.reaching-alpha-chi",
      "fields": {
        "title": {
          "text": "Can an experiment reach $\\alpha \\chi^{2/3}$ above one before radiation losses?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Reaching $\\chi \\sim \\alpha^{-3/2} \\sim 1600$ needs $\\gamma E/E_S \\sim 10^{3}$ ($E_S = m^2 c^3/(e \\hbar) \\sim 4.4 \\times 10^{13}\\,\\mathrm{statvolt}/\\mathrm{cm}$), but radiation reaction lowers gamma before the peak field is reached unless the interaction time is shorter than the radiation time. Determine whether any configuration, such as collisions of compressed $100\\,\\mathrm{GeV}$-class electron beams (Yakimenko et al. 2019), electron collisions with attosecond or tightly focused laser pulses, or aligned-crystal fields, yields a measurable number of events at $\\alpha \\chi^{2/3} \\ge 1$ with an identified observable that distinguishes nonperturbative from perturbative predictions. An answer is a start-to-end design with event rates, or a proof that radiation losses forbid it.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.stellarator-optimization.coil-complexity",
      "fields": {
        "precise": {
          "text": "Quantify the trade-off between quasisymmetry error and coil engineering metrics: minimum coil-plasma distance relative to minor radius, maximum coil curvature, number of coils and allowed fabrication tolerance. For example, determine whether planar or other simple coil sets can achieve quasisymmetry error below $10^{-2}$ at reactor aspect ratio and coil-plasma spacing. An answer is a Pareto frontier from global optimization.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.stellarator-optimization.qs-beta-stability",
      "fields": {
        "precise": {
          "text": "Quasisymmetry ($\\left|B\\right|$ depending on flux-surface angles only through one fixed linear combination) was achieved in vacuum with symmetry-breaking amplitude about $5 \\times 10^{-5}$ of the field strength (about $0.5\\,\\mathrm{G}$ in a $10^{4}\\,\\mathrm{G}$ field; Landreman and Paul, 2022). Determine whether equilibria exist with quasisymmetry error below $10^{-3}$, volume-averaged $\\beta$ of at least $5\\%$, ideal-MHD ballooning and kink stability, and nested flux surfaces, and map the trade-off frontier between these quantities. An answer is explicit configurations or a demonstrated frontier.",
          "how": [
            "inside:percent",
            "outside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.tokamak-confinement.density-limit",
      "fields": {
        "precise": {
          "text": "Discharges disrupt or return to L-mode when line-averaged density approaches the Greenwald density $n_G = 10^{14}\\,\\mathrm{cm}^{-3} x (I_p / 1\\,\\mathrm{MA}) / (\\pi (a / 100\\,\\mathrm{cm})^2)$, with $I_p$ the plasma current and a the minor radius. Identify the mechanism (edge turbulence transition at critical collisionality or adiabaticity, radiative collapse and MARFE formation, tearing-island growth, plasma-wall self-organization) and derive whether the maximum density scales with heating power and wall conditions. An answer is a predictive criterion validated on several devices, including cases with $n/n_G$ above 1.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.tokamak-confinement.lh-transition-mechanism",
      "fields": {
        "precise": {
          "text": "In diverted tokamaks, identify the mechanism that suppresses edge turbulence at the L-H transition within about $10^{-4}$ s: turbulence-driven zonal flows, the ion-diamagnetic radial electric field well, X-point ion orbit loss, or their combination. An answer is a flux-driven first-principles model (gyrokinetic or two-fluid, realistic diverted geometry) that reproduces the measured threshold power and its dependences on density, toroidal field direction, isotope and divertor geometry.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.vacuum-birefringence-schwinger.dynamically-assisted",
      "fields": {
        "precise": {
          "text": "The Schwinger rate in a constant field, $w = (e E)^2/(4\\pi^3 \\hbar^2 c)\\exp(-\\pi E_S/E)$ with $E_S \\sim 4.4 \\times 10^{13}\\,\\mathrm{statvolt}/\\mathrm{cm}$, is negligible at the $E/E_S \\sim 10^{-3}$ of present peak laser fields (peak intensity about $10^{30}\\,\\mathrm{erg}\\,\\mathrm{s}^{-1}\\,\\mathrm{cm}^{-2}$, approximate), where $\\exp(-\\pi E_S/E) \\sim \\exp(-3000)$. Superposing a weak high-frequency field (dynamically assisted Schwinger mechanism, Schuetzhold, Gies and Dunne 2008) reduces the exponent. For realistic focused optical pulses combined with XFEL or gamma-ray photons, determine the minimal strong-field intensity at which the nonperturbative assisted yield reaches 1 pair per shot, and specify an observable that separates it from perturbative multiphoton Breit-Wheeler pairs.",
          "how": [
            "inside:e-notation",
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.vacuum-birefringence-schwinger.static-field-birefringence",
      "fields": {
        "precise": {
          "text": "For a static field $B \\ll B_S = m^2 c^3/(e\\hbar) \\sim 4.4 \\times 10^{13}\\,\\mathrm{G}$, QED predicts $\\Delta n = n_{\\mathrm{par}} - n_{\\mathrm{perp}} = (\\alpha/(30\\pi))(B/B_S)^2$, about $4 \\times 10^{-24}$ at $B = 10^{4}\\,\\mathrm{G}$. Determine whether a Fabry-Perot ellipsometer with rotating or modulated fields of $10^{4}-10^{5}\\,\\mathrm{G}$ can reach this value with $\\text{signal-to-noise} > 5$, by identifying and suppressing the excess low-frequency noise that limited previous experiments, and measure $\\Delta n$ to within 10%.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "PVLAS ended in 2020 with $\\Delta n = (12 \\pm 17)e-23$ at $B = 2.5 \\times 10^{4}\\,\\mathrm{G}$, a $1\\,\\sigma$ uncertainty about 7 times the QED value $2.5 \\times 10^{-23}$ (Ejlli et al., Physics Reports 2020).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.vacuum-birefringence-schwinger.tunneling-breit-wheeler",
      "fields": {
        "settled_by": {
          "text": "A positron-yield scan versus laser intensity with calibrated gamma spectrum showing the $\\exp(-8/(3\\chi_{\\gamma}))$ dependence.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.vacuum-birefringence-schwinger.xfel-laser-birefringence",
      "fields": {
        "title": {
          "text": "First $5-\\sigma$ vacuum birefringence detection with an x-ray laser and optical laser",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.wakefield-accelerators.positron-acceleration",
      "fields": {
        "precise": {
          "text": "In the nonlinear blowout regime, plasma electrons are expelled and the ion column focuses electrons but defocuses positrons. Find a wake configuration (hollow channel, finite-radius plasma, electron filament, magnetized wake, quasi-linear wake) that simultaneously gives gradient above $10^{7}\\,\\mathrm{eV}/\\mathrm{cm}$, energy-transfer efficiency above 30 percent, rms energy spread below 1 percent and collider-level emittance preservation. An answer is a demonstrated configuration or a proof that the requirements are incompatible.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "plasma.warm-dense-matter.carbon-gbar-eos",
      "fields": {
        "precise": {
          "text": "Along the principal Hugoniot of carbon and CH at pressures $10^{14}\\ \\text{to}\\ 10^{16}\\ \\mathrm{dyn}/\\mathrm{cm}^{2}$ $(0.1\\ \\text{to}\\ 10\\ \\mathrm{Gbar})$, K-shell and L-shell ionization produce a maximum in shock compression $\\rho/\\rho_{0}$; average-atom, path-integral Monte Carlo and DFT-MD equations of state differ in the height and pressure of this maximum. Determine $\\rho/\\rho_{0}$ versus pressure to within $3\\%$ across this range and identify which theory reproduces it. An answer is a Hugoniot measurement with that precision plus a theory matching it.",
          "how": [
            "inside:e-notation",
            "inside:percent"
          ]
        },
        "settled_by": {
          "text": "Laser- or pulsed-power-driven Hugoniot measurements at $10^{14}\\text{ to }10^{16}\\ \\mathrm{dyn}/\\mathrm{cm}^{2}$ with density uncertainty near 3 percent, matched by one first-principles equation of state.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.cft-rg.five-d-on",
      "fields": {
        "title": {
          "text": "Does an interacting unitary O(N) CFT exist in five dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.cft-rg.nonsusy-conformal-manifold",
      "fields": {
        "title": {
          "text": "Do non-supersymmetric conformal manifolds exist above two dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.adiabatic-continuity",
      "fields": {
        "title": {
          "text": "Does small-circle semiclassical confinement connect smoothly to four dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.center-vortex-dominance",
      "fields": {
        "title": {
          "text": "Do center vortices alone give the full SU(3) string tension?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.chiral-from-confinement",
      "fields": {
        "title": {
          "text": "Does confinement imply chiral symmetry breaking in QCD-like theories?",
          "how": [
            "title:question-mark"
          ]
        },
        "status_note": {
          "text": "Ciambriello, Contino, Luzio, Romano and Xu (2024, arXiv:2404.02967) proved breaking for $N_{f} \\ge p_{\\min}$, the smallest prime factor of $N_{c}$; smaller $N_{f}$ requires assuming no phase transition as quark masses are sent to infinity.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.k-string-tensions",
      "fields": {
        "precise": {
          "text": "In $4\\mathrm{D}$ $\\mathrm{SU}(N)$ Yang-Mills let $\\sigma_k$ be the asymptotic string tension between static sources of N-ality k. Determine $\\sigma_k/\\sigma_1$ at large N, in particular whether corrections to the free-string value k are of order $1/N$ (Casimir scaling, $k(N-k)/(N-1)$) or of order $1/N^{2}$ (sine law, $\\sin(\\pi k/N)/\\sin(\\pi/N)$), or follow neither form.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.mechanism",
      "fields": {
        "title": {
          "text": "Which gluon field configurations cause quark confinement?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.theta-pi-su2",
      "fields": {
        "precise": {
          "text": "In $4\\mathrm{D}$ $\\mathrm{SU}(N)$ Yang-Mills with topological angle $\\theta$, the mixed anomaly between the $Z_{N}$ one-form center symmetry and CP at $\\theta = \\pi$ (Gaiotto, Kapustin, Komargodski, Seiberg 2017) forbids a trivially gapped confining vacuum. For $N = 2$, determine whether the vacuum at $\\theta = \\pi$ breaks CP spontaneously (two degenerate vacua and a first-order jump of the topological charge density), is deconfined (including gapped with topological order), or is gapless. Large-N arguments favor CP breaking.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.confinement.worldsheet-axion",
      "fields": {
        "precise": {
          "text": "Lattice spectra of closed flux tubes in $4\\mathrm{D}$ $\\mathrm{SU}(N)$ Yang-Mills ($N = 3, 5, 6$) are fitted by an effective string of two transverse phonons plus a massive pseudoscalar worldsheet axion coupled to the phonons through a topological term (Dubovsky, Flauger, Gorbenko 2013; Athenodorou, Dubovsky, Luo, Teper 2024). Determine the $N \\to \\infty$ limits of the axion mass $m_a/\\sqrt{\\sigma}$ and its coupling, and whether the large-N worldsheet theory is the integrable axionic string constructed by Dubovsky and Gorbenko (2015).",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.double-copy.n8-finiteness",
      "fields": {
        "title": {
          "text": "Is four-dimensional $N=8$ supergravity ultraviolet finite at seven loops?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.generalized-symmetries.gaplessness",
      "fields": {
        "title": {
          "text": "When do non-invertible symmetries forbid a featureless gapped phase?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.gravity-positivity.allowed-negativity",
      "fields": {
        "title": {
          "text": "How negative can forward-limit coefficients be once gravity is included?",
          "how": [
            "title:owner"
          ]
        },
        "precise": {
          "text": "For a weakly coupled 4D effective field theory of a massless scalar coupled to Einstein gravity, with $2\\to 2$ amplitude $M(s,t) = 8\\pi G s^2/(-t) + c_2 s^2/\\Lambda^4 + ...$, determine the lowest value of $c_2$ consistent with unitarity, analyticity, crossing and a UV completion whose amplitude Reggeizes (grows as $s^{2 + \\alpha' t}$) above a scale $M_*$. Under this Regge assumption proposals give $c_2 \\ge -\\operatorname{O}(\\Lambda^4/(M_{\\mathrm{pl}}^2 M_*^2))$; smeared impact-parameter sum rules in $D = 4$ instead give $c_2 \\ge -\\operatorname{O}(G \\Lambda^4/M^2)\\log(M b_{\\mathrm{IR}})$, where $M$ is the EFT cutoff and $b_{\\mathrm{IR}}$ an infrared impact-parameter cutoff. An answer is the optimal bound in $D = 4$ with its assumptions stated, saying which form is optimal, or an explicit consistent UV completion that violates it.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.gravity-positivity.qed-new-physics",
      "fields": {
        "title": {
          "text": "Does electromagnetism plus gravity require new particles far below the Planck scale?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "For QED with electron mass $m_{e}$ and charge $e$ coupled to gravity, the one-loop light-by-light and gravitational contributions to the forward photon-photon amplitude violate the naive positivity bound unless new states appear at $\\Lambda_{\\mathrm{new}}\\sim(e\\,m_{e}\\,M_{\\mathrm{pl}})^{1/2}$, approximately $2 \\times 10^{7}\\ \\text{to}\\ 4 \\times 10^{7}\\ \\mathrm{GeV}$ (reduced or unreduced Planck mass) (Alberte, de Rham, Jaitly, Tolley, Phys. Rev. D 103, 125020, 2021, obtained assuming the t-channel graviton pole can be discarded). Decide whether every consistent UV completion of QED plus gravity has new states below this scale, or whether the allowed Planck-suppressed negativity removes the requirement.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.lattice-chiral.mirror-decoupling",
      "fields": {
        "title": {
          "text": "Can interactions decouple mirror fermions in lattice chiral theories?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.massless-bootstrap.large-n-pion-kink",
      "fields": {
        "title": {
          "text": "Does large-N QCD lie at the pion bootstrap kink?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.non-ads-holography.carrollian-dual",
      "fields": {
        "title": {
          "text": "Is 4D flat-space gravity dual to a 3D Carrollian field theory?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.non-ads-holography.celestial-cft",
      "fields": {
        "title": {
          "text": "Is there a consistent celestial CFT for four-dimensional gravity?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.non-ads-holography.flat-limit",
      "fields": {
        "title": {
          "text": "Does the flat-space limit of AdS/CFT define the full S-matrix?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.nonlagrangian.6d-scft-completeness",
      "fields": {
        "title": {
          "text": "Do all six-dimensional superconformal theories arise from F-theory?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.resurgence.adler-transseries",
      "fields": {
        "title": {
          "text": "Does QCD perturbation theory plus condensates resum to the exact answer?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.resurgence.renormalon-semiclassics",
      "fields": {
        "precise": {
          "text": "In asymptotically free theories ($4\\mathrm{D}$ Yang-Mills and QCD, $2\\mathrm{D}$ $\\mathrm{O}(N)$, $\\mathrm{CP}^{N-1}$ and principal chiral models), the Borel transform of perturbation series has renormalon singularities at positions set by the one-loop beta-function coefficient, not matched by any finite-action classical solution. Identify the nonperturbative sectors (saddles, fractional instantons, bions on R^{d-1} x S^1, or OPE condensates) whose imaginary ambiguities cancel the renormalon ambiguities, and demonstrate the cancellation.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.rg-irreversibility.f-theorem-5d",
      "fields": {
        "title": {
          "text": "Does the sphere free energy decrease along five-dimensional RG flows?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.rg-irreversibility.scale-vs-conformal",
      "fields": {
        "title": {
          "text": "Does scale invariance imply conformal invariance in four dimensions?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.rg-irreversibility.six-d-a-theorem",
      "fields": {
        "title": {
          "text": "Does the a-anomaly decrease along all six-dimensional RG flows?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.rg-irreversibility.strong-a-gradient",
      "fields": {
        "title": {
          "text": "Is four-dimensional RG flow a gradient flow of the a-function?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.spacetime-entanglement.holographic-cft-criteria",
      "fields": {
        "title": {
          "text": "Which conformal field theories have a semiclassical gravity dual?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.string-nonperturbative.bfss-lorentz",
      "fields": {
        "title": {
          "text": "Does BFSS matrix theory recover eleven-dimensional Lorentz invariance?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.string-nonperturbative.ikkt-four-dims",
      "fields": {
        "title": {
          "text": "Do four expanding spacetime dimensions emerge in the IKKT model?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.string-vacua.6d-string-universality",
      "fields": {
        "title": {
          "text": "Is every anomaly-free six-dimensional supergravity realized in string theory?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.string-vacua.ds-vacua-existence",
      "fields": {
        "title": {
          "text": "Does string theory have controlled metastable de Sitter vacua?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.string-vacua.landscape-finiteness",
      "fields": {
        "title": {
          "text": "Is the number of string vacua finite?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.swampland.ds-conjecture",
      "fields": {
        "precise": {
          "text": "The refined de Sitter conjecture (2018) states that in asymptotic, weakly coupled regions of moduli space, $\\mid \\operatorname{grad} V \\mid \\ge c V/M_{P}$ or $\\mathrm{min}\\ \\mathrm{eigenvalue}(\\operatorname{grad}\\ \\operatorname{grad} V) \\le -c' V/M_P^{2}$ with c, c' of order 1. Determine whether this holds in all asymptotic regions of string moduli spaces and find the optimal value of c in d dimensions.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.swampland.emergent-strings",
      "fields": {
        "title": {
          "text": "Is every infinite-distance limit a decompactification or a weak string?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qft.swampland.weak-gravity",
      "fields": {
        "title": {
          "text": "Does the weak gravity conjecture hold in all quantum gravity theories?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.classical-simulability.barren-plateau-simulability",
      "fields": {
        "title": {
          "text": "Does absence of barren plateaus imply classical simulability?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.classical-simulability.t-state-stabilizer-rank",
      "fields": {
        "precise": {
          "text": "The stabilizer rank $\\chi(\\psi)$ is the least number of stabilizer states whose linear combination equals $\\psi$. Prove $\\chi(\\left|T\\right>^{\\otimes n}) \\ge 2^{c n}$ for some constant $c > 0$, where $\\left|T\\right> = (\\left|0\\right> + e^{i \\pi/4} \\left|1\\right>)/\\sqrt{2}$. Known upper bounds are of order $2^{0.4 n}$ (approximate exponent) and known lower bounds are only polynomial in n.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.collapse-models.diosi-penrose-test",
      "fields": {
        "precise": {
          "text": "In the Diosi-Penrose model a superposition decays at rate $\\Gamma = E_G / \\hbar$, with $E_G$ the gravitational self-energy of the difference of the two mass distributions, regularized by a length $R_0$. X-ray bounds give $R_0 > 4.9 \\times 10^{-8}\\,\\mathrm{cm}$ (XENONnT, 90 percent C.L.) for the Markovian version. Determine whether a superposition experiment, or a non-radiating dissipative version of the model, can reach the regime where $\\Gamma$ exceeds all environmental decoherence for allowed $R_0$, and measure or exclude it.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "Underground X-ray searches (Donadi et al., Nature Physics 2021; XENONnT, Phys. Rev. Lett. 136, 120201, 2026) excluded the Markovian model with $R_0$ below about $5 \\times 10^{-8}\\,\\mathrm{cm}$, about fivefold beyond the previous Majorana Demonstrator bound; larger $R_0$ and dissipative versions are untested.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.collapse-models.markovian-csl-window",
      "fields": {
        "precise": {
          "text": "Markovian (white-noise) CSL has collapse rate $\\lambda$ and correlation length $r_{C}$. X-ray spontaneous emission in XENONnT gives $\\lambda / r_{C}^{2} < 3.0 \\times 10^{-7}\\,\\mathrm{s}^{-1}\\,\\mathrm{cm}^{-2}$ (90 percent C.L.) for $r_{C}$ below about $10^{-3}\\,\\mathrm{cm}$; mechanical and interferometric bounds cover larger $r_{C}$. Theoretical lower bounds require collapse of a barely visible object within about $10^{-2}\\,\\mathrm{s}$. Determine whether the region between experimental upper bounds and theoretical lower bounds is empty for all $r_{C}$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "XENONnT (Phys. Rev. Lett. 136, 120201, 2026) excluded the GRW values $\\lambda = 10^{-16}\\ \\mathrm{s}^{-1}$, $r_{C} = 10^{-5}\\ \\mathrm{cm}$ at $9.1\\sigma$, improving the previous X-ray bound about 135-fold.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.contextuality-nonlocality.i3322-finite-dimension",
      "fields": {
        "precise": {
          "text": "For the Collins-Gisin $I3322$ Bell functional (two parties, three two-outcome measurements each), determine whether the supremum over tensor-product quantum strategies, approximately 0.25087538 (Pal and Vertesi, PRA 2010), is attained by any finite-dimensional strategy, and how the local dimension needed to come within $\\epsilon$ of it grows. The residual task is verification of the 2026 claims: non-attainment in finite dimension, attainment by an infinite-dimensional strategy on $\\ell^{2}(Z) x \\ell^{2}(Z)$, and required dimension of order $\\log(1/\\epsilon)$.",
          "how": [
            "inside:operator-word",
            "ai:gpt-5.5"
          ]
        },
        "status_note": {
          "text": "Two independent preprints of August-September 2026 claim non-attainment in finite dimension (Douglas, arXiv:2609.05555; Krohn-Grimberghe, arXiv:2609.29693, computer-assisted, value bracketed to width $10^{-55}$); neither is refereed.",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.contextuality-nonlocality.tsirelson-explicit-game",
      "fields": {
        "precise": {
          "text": "$\\mathrm{MIP}* = \\mathrm{RE}$ (Ji, Natarajan, Vidick, Wright, Yuen, arXiv:2001.04383) implies a nonlocal game $G$ with finite inputs and outputs whose commuting-operator value $w_{qc}(G)$ exceeds its tensor-product value $w_{q}(G)$, resolving Tsirelson's problem negatively. Construct an explicit $G$, state its input size and gap, and certify $w_{qc}(G) > w_{q}(G)$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.contextuality-nonlocality.werner-povm-locality",
      "fields": {
        "precise": {
          "text": "Let $v_c^{\\mathrm{POVM}}$ be the critical visibility of $\\rho_W(v)$ under arbitrary local POVMs. Known: $\\rho_W(v)$ is local for all POVMs when $v \\le 1/2$ (Zhang and Chitambar, arXiv:2309.09960) and for projective measurements when $v \\le 0.6875$. Determine whether $v_c^{\\mathrm{POVM}}$ equals the projective threshold $v_c$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.fault-tolerance-noise.exponential-suppression-scaling",
      "fields": {
        "title": {
          "text": "Does logical error suppression continue exponentially to large code distance?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.fault-tolerance-noise.long-range-correlated-threshold",
      "fields": {
        "precise": {
          "text": "Qubits on a $D$-dimensional lattice couple through $H_{\\int} = \\sum_i \\sigma_i B_i$ to a Gaussian bath with fixed single-qubit noise strength $\\langle B_i B_i\\rangle$ and spatial correlations $\\langle B_i(t) B_j(t')\\rangle$ decaying as $\\left|r_i - r_j\\right|^{-\\alpha}$. A threshold is proved when the system-bath coupling decays faster than $1/r^D$ (Aharonov, Kitaev and Preskill, Phys. Rev. Lett. 96, 050504, 2006, arXiv:quant-ph/0510231). Decide whether a positive threshold in the single-qubit noise strength exists for $\\alpha \\le D$, or prove a logical-error floor independent of code size.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.fault-tolerance-noise.surface-code-hashing-bound",
      "fields": {
        "title": {
          "text": "Does the optimal toric-code depolarizing threshold equal the hashing bound?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.gravity-quantum.gme-interpretation",
      "fields": {
        "precise": {
          "text": "The LOCC argument (local operations and classical communication cannot create entanglement) assumes the gravitational mediator acts as a classical channel. Determine under which explicit assumptions (locality, field-theoretic matter, linearity) observed entanglement at the rate $\\phi = G m^2 t/(\\hbar d)$ excludes classical gravity, and compute the entanglement producible by semiclassical or stochastic classical gravity coupled to quantum-field matter, which Aziz and Howl find enters at higher order in G and grows with mass toward the Planck mass (about $2 \\times 10^{-5}$ g).",
          "how": [
            "outside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.gravity-quantum.gme-observation",
      "fields": {
        "precise": {
          "text": "Two masses $m \\sim 10^{-11}\\,\\mathrm{g}$, each in a spatial superposition of size $\\Delta x \\sim 2.5 \\times 10^{-2}\\,\\mathrm{cm}$ at separation $d \\sim 4.5 \\times 10^{-2}\\,\\mathrm{cm}$, acquire branch-dependent phases $\\phi = G m^{2} t / (\\hbar d)$ over $t \\sim 2.5\\,\\mathrm{s}$ (illustrative parameters of Bose et al. 2017, approximate). Demonstrate a positive entanglement witness (e.g. embedded-spin correlations) with Casimir-Polder and electromagnetic couplings suppressed below the gravitational one and decoherence rates below $1/t$.",
          "how": [
            "inside:e-notation"
          ]
        },
        "status_note": {
          "text": "As of 2026 no spatial superposition of a mass near $10^{-11}\\,\\mathrm{g}$ has been made; 2026 analyses give witness values of order $-10^{-2}$ for $m = 10^{-11}\\,\\mathrm{g}$ over 0.1 s with decoherence rates of $0.1 \\text{ to } 1\\,\\mathrm{s}^{-1}$ (arXiv:2609.10697).",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.gravity-quantum.superposed-source-gravity",
      "fields": {
        "precise": {
          "text": "Prepare a source mass $M$ in a spatial superposition of separation $\\Delta x$ and measure a probe's response that distinguishes a field sourced by the expectation value $\\langle T_{00}\\rangle$ (Moller-Rosenfeld semiclassical gravity) from a branch-correlated field, at force scale $\\sim G M m_{\\mathrm{probe}} \\Delta x / d^3$. Required: source masses small enough to superpose ($M <\\sim 10^{-11}\\,\\mathrm{g}$) and probe force sensitivity at that scale.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.hamiltonian-complexity.commuting-hamiltonian-np",
      "fields": {
        "title": {
          "text": "Is the commuting local Hamiltonian problem in NP?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Given $H = \\sum_i h_i$ with pairwise commuting k-local projectors $h_i$ on qudits of dimension $q$, decide whether the ground energy is 0 or at least $1/\\operatorname{poly}(n)$. Is this in NP for all constant k and q? Known in NP: 2-local (Bravyi and Vyalyi 2003), some 3-local cases (Aharonov and Eldar 2011), $2\\mathrm{D}$ qubits (Schuch 2011), $2\\mathrm{D}$ qutrits and factorized terms of any dimension (Irani and Jiang, arXiv:2309.04910).",
          "how": [
            "inside:operator-word",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.hamiltonian-complexity.quantum-pcp-conjecture",
      "fields": {
        "precise": {
          "text": "Let $H = \\sum_{i=1}^m H_i$ be a $k$-local Hamiltonian on $n$ qubits with $\\mid\\mid H_i\\mid\\mid \\le 1$ and each qubit in $O(1)$ terms. Is it QMA-hard to approximate its ground energy to additive error $\\epsilon m$ for some constant $\\epsilon > 0$? An answer is a proof of QMA-hardness, or a proof that the problem lies in NP (or a smaller class).",
          "how": [
            "inside:operator-word",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.macro-superpositions.leggett-garg-massive",
      "fields": {
        "precise": {
          "text": "For a mechanical mode of effective mass $m\\ge 10^{-6}\\,\\mathrm{g}$, measure two-time correlators $C_{ij}$ of a two-valued observable at $t_1<t_2<t_3$ and test $K=C_{12}+C_{23}-C_{13}\\le 1$, using ideal negative-result or control-experiment protocols that close the clumsiness loophole (disturbance by the measurement itself). An answer is $K>1$ at stated significance with invasiveness bounded by independent controls.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.macro-superpositions.levitated-nanoparticle-superposition",
      "fields": {
        "precise": {
          "text": "For an optically or magnetically levitated dielectric particle of mass about $10^{-15} \\text{ to } 10^{-14}\\,\\mathrm{g}$ (radius $r \\sim 5 \\times 10^{-6} \\text{ to } 10^{-5}\\,\\mathrm{cm}$) prepared near its motional ground state, create a coherent spatial superposition or wave packet with coherence length exceeding $r$, and verify coherence by interference fringes or Wigner-function negativity, since position variance alone does not distinguish coherent from incoherent spreading.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.macro-superpositions.megadalton-interference",
      "fields": {
        "precise": {
          "text": "Demonstrate near-field (Talbot-Lau) or far-field interference of neutral particles of mass $m \\ge 10^{6}\\,\\mathrm{u}$ ($1.7 \\times 10^{-18}\\,\\mathrm{g}$) whose visibility versus grating power follows the quantum prediction and excludes the classical moire-shadow prediction at stated confidence, and report $\\mu$. The 2025 analysis indicates metal clusters need velocities near $2.5 \\times 10^{3}\\,\\mathrm{cm}/\\mathrm{s}$ in a $10^{2}\\,\\mathrm{cm}$ scale interferometer.",
          "how": [
            "inside:e-notation"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.measurement-problem.definite-outcomes",
      "fields": {
        "precise": {
          "text": "For a system $S$ in state $\\sum_{k} c_k |k>$ coupled unitarily to apparatus $A$ and environment $E$, unitary evolution gives $\\sum_{k} c_k |k>|A_k>|E_k>$; decoherence makes the reduced density matrix of $S+A$ diagonal but selects no single $k$. Required: a modified dynamics, an added ontology (hidden variables, branches) or a principled account that yields single outcomes with frequencies $\\mid c_k\\mid^2$, together with either predictions that differ from standard quantum mechanics or a proof of empirical equivalence. This is the root problem of the topic; its workable sharper forms are listed under related.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.monitored-circuits.monitored-free-fermions-1d",
      "fields": {
        "title": {
          "text": "Does a critical phase exist for monitored free fermions in one dimension?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.monitored-circuits.postselection-free-observation",
      "fields": {
        "precise": {
          "text": "For non-Clifford monitored circuits on $N$ qubits under Born-rule measurements, find an estimator that detects $p_c$ with $\\operatorname{poly}(N)$ samples and $\\operatorname{poly}(N)$ classical processing, or prove that every such probe needs $\\exp(N)$ resources. Known probes use Clifford circuits, require classically simulating the circuit (cross-entropy benchmark of Li, Zou, Glorioso, Altman and Fisher, PRL 130, 220404, 2023), or postselect.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.qldpc-codes.constant-overhead-ft",
      "fields": {
        "precise": {
          "text": "For quantum circuits on $N$ logical qubits of depth $\\operatorname{poly}(N)$ under local stochastic noise below a constant threshold, does a fault-tolerance scheme exist with physical-to-logical qubit ratio $O(1)$ and time overhead $O(1)$? Gottesman (2013) gave constant space with polynomial time overhead; schemes from 2024 reach constant space with polylogarithmic or $O \\sim (\\mathrm{log} N)$ time overhead (arXiv:2411.03632, arXiv:2411.03683). An answer is a construction or a lower bound proving that $\\omega(1)$ time overhead is necessary at constant space overhead.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-chemistry-algorithms.exponential-advantage-chemistry",
      "fields": {
        "title": {
          "text": "Is there exponential quantum advantage for molecular ground-state energies?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-chemistry-algorithms.hubbard-resource-estimate",
      "fields": {
        "precise": {
          "text": "For the $2\\mathrm{D}$ Fermi-Hubbard model at $U/t = 8$ and hole doping near $1/8$ on L x L lattices, determine the minimum logical qubit count and Toffoli count for phase estimation to give the energy per site to accuracy $10^{-3} t$ at a size L beyond reliable classical extrapolation, including state-preparation cost. Published estimates (e.g. Kivlichan et al., Quantum 2020) give roughly $10^{6}-10^{8}$ Toffoli gates for lattices of about $10 \\times 10 \\text{ to } 20 \\times 20$ sites, without full overlap costs (figures approximate).",
          "how": [
            "inside:x-times",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-shannon-theory.depolarizing-capacity-threshold",
      "fields": {
        "precise": {
          "text": "For the qubit depolarizing channel $D_p(\\rho) = (1 - p) \\rho + (p/3)(X \\rho X + Y \\rho Y + Z \\rho Z)$, find $p*$ with quantum capacity $Q(D_p) > 0$ if and only if $p < p*$. Known: $Q = 0$ for $p \\ge 1/4$; the hashing bound is positive up to $p \\sim 0.1893$, and degenerate codes push positivity above 0.19 (DiVincenzo, Shor and Smolin 1998; Smith and Smolin 2007), with further small improvements since. More generally, compute $Q(D_p)$ for any $0 < p < 1/4$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-shannon-theory.npt-bound-entanglement",
      "fields": {
        "title": {
          "text": "Do bound entangled states with negative partial transpose exist?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Does there exist a bipartite state $\\rho$ on $C^{d}\\,\\otimes\\,C^{d}$, $d \\ge 3$, with negative partial transpose $\\rho^{\\Gamma}$ that is not distillable, i.e. for every n and all rank-2 projectors P, Q on the n-copy spaces, $(P\\,\\otimes\\,Q)(\\rho^{\\Gamma})^{\\otimes\\,n}(P\\,\\otimes\\,Q) \\ge 0$? It suffices to decide this for Werner states $\\rho(d, \\alpha) = (1 + \\alpha V)/(d^{2} + \\alpha d)$, $V$ the swap operator, with $-1/2 \\le \\alpha < -1/d$ (for $\\alpha < -1/2$ the state is already 1-copy distillable).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-shannon-theory.quantum-capacity-computability",
      "fields": {
        "title": {
          "text": "Is the quantum capacity of a channel computable?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "$Q(N) = \\lim_{n \\to \\infty} (1/n) \\max_\\rho I_c(\\rho, N^{(\\otimes\\ n)})$, with $I_c$ the coherent information. Is there an algorithm that, given a channel N with rational Kraus operators and $\\epsilon > 0$, outputs $Q(N)$ to within $\\epsilon$, or that decides whether $Q(N) > 0$? Cubitt et al. (Nat. Commun. 6, 7739, 2015, arXiv:1408.5115) showed that for every n there are channels with zero n-use coherent information and positive capacity.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-shannon-theory.werner-two-copy",
      "fields": {
        "precise": {
          "text": "Show that the $d = 4$ Werner state $\\rho(4, -1/2)$ is not 2-copy distillable: for all rank-2 projectors P, Q acting on two copies of each party's space, $\\left(P\\,\\otimes\\,Q\\right)\\left[(\\rho^\\Gamma)^{\\otimes 2}\\right]\\left(P\\,\\otimes\\,Q\\right)$ has no negative eigenvalue; or exhibit P, Q giving a negative eigenvalue. Its partial transpose is proportional to a unitary (Problem 5 of Horodecki, Rudnicki and Zyczkowski 2022).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.quantum-thermo.strong-coupling-heat-work",
      "fields": {
        "precise": {
          "text": "For $H = H_S(t) + H_B + H_I$ with the norm of $H_I$ comparable to the system energy scale, find definitions of internal energy $U$, work $W$ and heat $Q$ of the system that satisfy the first law, a second law (Clausius inequality or nonnegative entropy production), reduce to weak-coupling results, and are measurable by local operations; or prove that no definition satisfies all of these.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.qubit-platform-limits.correlated-error-bursts",
      "fields": {
        "title": {
          "text": "Can radiation-induced error bursts in superconducting chips be made rare enough?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.self-correcting-memory.three-dimensional-existence",
      "fields": {
        "precise": {
          "text": "Does there exist a family of geometrically local Hamiltonians on qubits in $R^{3}$, with bounded interaction strength and qubit density, whose ground space encodes at least one qubit with a memory time, under a weakly coupled thermal bath (Davies dynamics), that grows as $\\exp(c L^{b})$, $b > 0$, at some fixed temperature $T > 0$?",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.self-correcting-memory.two-dimensional-no-go",
      "fields": {
        "title": {
          "text": "Is self-correction impossible for every two-dimensional local Hamiltonian?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.sic-mub.mub-composite-max",
      "fields": {
        "precise": {
          "text": "Let $N(d)$ be the maximal number of MUBs in $C^d$, with $N(d) = d + 1$ for prime powers. Determine whether $N(d) < d + 1$ for every d that is not a prime power, and find $N(d)$ for $d = 10\\text{ and }12$. Lower bounds exceed the tensor-product bound $1 + \\min_i p_i^{a_i}$ in some dimensions, e.g. five MUBs in $d = 12$ (Cardenes Wuttig and Tindall, arXiv:2609.40311, 2026).",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.sic-mub.mub-dimension-six",
      "fields": {
        "title": {
          "text": "Do four mutually unbiased bases exist in dimension six?",
          "how": [
            "title:question-mark"
          ]
        },
        "precise": {
          "text": "Do there exist four orthonormal bases of $C^6$ such that $\\left|\\langle a \\mid b\\rangle\\right|^2 = 1/6$ for any vectors a, b taken from different bases? Three are known; numerics and partial classifications of $6 \\times 6$ complex Hadamard matrices suggest that four do not exist.",
          "how": [
            "inside:x-times"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.sic-mub.sic-existence",
      "fields": {
        "title": {
          "text": "Do SIC-POVMs exist in every finite dimension?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.tunneling-arrival-time.attoclock-delay",
      "fields": {
        "precise": {
          "text": "In elliptically polarized strong-field ionization of atomic hydrogen or helium, extract the tunneling delay $\\tau_T$ from the photoelectron momentum offset angle after subtracting the Coulomb deflection computed from the full time-dependent Schrodinger equation, and decide whether $\\tau_T = 0$ within resolution. A 2019 hydrogen experiment (Sainadh et al., Nature) reported $\\tau_{T}$ below about $1.8 \\times 10^{-18}\\,\\mathrm{s}$.",
          "how": [
            "inside:e-notation",
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.useful-advantage.dqi-optimization-speedup",
      "fields": {
        "title": {
          "text": "Can classical algorithms match decoded quantum interferometry on polynomial intersection?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "qi.useful-advantage.otoc-beyond-classical",
      "fields": {
        "title": {
          "text": "Is the 2025 OTOC(2) quantum echo experiment beyond classical simulation?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.absorbing-states-soc.dp-exact-exponents",
      "fields": {
        "precise": {
          "text": "For $1+1$ dimensional directed percolation (bond, site, or the contact process), determine exact values of $\\beta \\text{ approximately } 0.276486, \\nu_{\\mathrm{perp}} \\text{ approximately } 1.096854 \\text{ and } \\nu_{\\mathrm{par}} \\text{ approximately } 1.733847$, or show that they do not come from a solvable structure; the model is not known to be integrable and its critical point lacks conformal invariance in the usual sense because time and space scale differently. An answer is closed forms matching the series values.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.absorbing-states-soc.manna-class-identity",
      "fields": {
        "title": {
          "text": "Is the Manna class distinct from directed percolation?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.arrow-of-time.recollapse-arrow",
      "fields": {
        "title": {
          "text": "Does the thermodynamic arrow reverse in a recollapsing universe?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.extreme-events-predictability.finite-predictability-horizon",
      "fields": {
        "precise": {
          "text": "For flows with energy spectrum $E(k) \\sim k^{-\\beta}$ over an inertial range, Lorenz predicted that for $\\beta < 3$ the predictability time $T_p$ stays bounded as the initial error amplitude $\\delta_0 \\to 0$ at fixed error scale, since error moves upscale in eddy turnover times $\\tau(k) \\sim k^{((\\beta-3)/2)}$. Determine whether this holds for 3D Navier-Stokes turbulence ($\\beta = 5/3$) as the Reynolds number grows, and how $T_p$, in units of the large-eddy turnover time, depends on the dissipation range and on the scale of the initial error. Answer: yes or no, with $T_p$ and its dependences.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.fput-thermalization.dnls-negative-temperature",
      "fields": {
        "precise": {
          "text": "For the DNLS chain $H = \\sum_n [ (\\psi_n* \\psi_{(n+1)} + \\mathrm{c.c.}) + (g/2)\\left|\\psi_n\\right|^4 ]$ with conserved norm density $a$ and energy density $h$ above the infinite-temperature line $h_{\\mathrm{inf}} = g a^2$, determine whether isolated dynamics from generic initial data relaxes to the microcanonical equilibrium (one breather holding a macroscopic fraction of the norm on an infinite-temperature background), and give the scaling of the relaxation time with chain length $N$ and with $h - h_{\\mathrm{inf}}$. An answer is the asymptotic law, or a proof that the relaxation time diverges with $N$.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.fput-thermalization.equipartition-time-scaling",
      "fields": {
        "precise": {
          "text": "For alpha- and beta-FPUT chains with $N$ particles at energy density $\\epsilon$ and effective nonlinearity g ($g \\sim \\alpha^2 \\epsilon \\text{ or } \\beta \\epsilon$), determine whether the equipartition time obeys $T_{\\mathrm{eq}} \\sim g^{-2}$ for $N > N*(g)$ in the thermodynamic limit, as wave-turbulence theory of resonant wave interactions predicts, and determine $N*(g)$ and the small-N regime where exact resonances are absent and the exponent differs. An answer is the exponent with its range of validity.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.ising-3d.rfim-dimensional-reduction",
      "fields": {
        "precise": {
          "text": "For the random-field Ising model with Gaussian random fields, Parisi-Sourlas supersymmetry predicts that critical exponents in dimension d equal those of the pure Ising model in $d - 2$. Determine the dimension $d_{\\mathrm{DR}}$ below which this dimensional reduction fails and the mechanism, a cusp in the renormalized disorder cumulants (functional RG, $d_{\\mathrm{DR}} \\text{ approximately } 5.1$) or new relevant operators (other RG analyses, $d_{\\mathrm{DR}}\\ \\text{between}\\ 4\\ \\text{and}\\ 5$).",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.kpz-higher-d.experiment-2plus1",
      "fields": {
        "precise": {
          "text": "Measure, in a $2+1$ dimensional KPZ system other than flat thin-film deposition (curved or stationary initial geometry, or the phase of a 2D driven-dissipative condensate), the one-point distribution of $\\chi$ and the spatial and two-time correlation functions, and compare them with simulated universal functions for that geometry (exponents $\\alpha \\text{ approximately } 0.39, z \\text{ approximately } 1.61$).",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.kpz-higher-d.exponents-2plus1",
      "fields": {
        "precise": {
          "text": "For the KPZ equation $dh/dt = \\nu \\mathrm{lap}\\ h + (\\lambda/2)(\\mathrm{grad}\\ h)^2 + \\eta(x,t)$ with Gaussian white noise $\\eta$ in $d = 2$ spatial dimensions, determine the roughness exponent $\\alpha$ (with $z = 2 - \\alpha$ from Galilean invariance) exactly or to $10^{-4}$, and decide whether it is a simple rational number. Large simulations give $\\alpha$ approximately 0.387 to 0.39; the conjecture $\\alpha = 2/5$ is disfavored.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.learning-inference.benign-interpolation-feature-learning",
      "fields": {
        "precise": {
          "text": "Two-layer network $f(x) = \\sum_{j=1..m} a_j \\sigma(w_j . x)$ trained by gradient descent from small initialization to zero training loss on n samples $y = f_{*}(x) + \\mathrm{noise}$ of variance $\\sigma_n^2$, $x \\sim \\mathrm{N}(0, I_d)$ with $I_d$ the d x d identity, in the limit $n, d \\to \\infty$ with $\\psi = n/d$ fixed and $m >> n$. For targets $f_{*}(x) = g(U x)$ with $U$ an r x d matrix and r fixed, compute the limiting test mean-squared error on noisy labels $E(\\psi, \\sigma_n^2, g)$ at fixed $\\psi$, and classify the interpolation by the $\\psi \\to \\infty$ limit of $E$: benign if $E \\to \\sigma_n^2$, tempered if $E \\to c\\,\\sigma_n^2$ with $1 < c < \\infty$, catastrophic if $E$ diverges. The answer is an asymptotic formula, proved or confirmed numerically to high precision.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.learning-inference.scaling-law-exponents",
      "fields": {
        "precise": {
          "text": "For a deep network trained in the feature-learning regime on natural data, the test loss follows $L($$N$, $D$$) = L_{\\infty} + A N^{-\\beta_N} + B D^{-\\beta_D}$ over several decades, with N parameters and D training examples or tokens. Derive $\\beta_N, \\beta_D$ and the compute-optimal allocation exponent from measurable statistics of the data distribution (for example the power-law decay exponent of the data covariance spectrum or of the target function's spectral decomposition). An answer is a theory that predicts measured exponents on a held-out dataset and architecture within quoted errors, or a proof that no data statistic of this kind fixes them.",
          "how": [
            "ai:gpt-5.5"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.learning-inference.sgd-multi-index-complexity",
      "fields": {
        "precise": {
          "text": "Inputs $x \\sim N(0, I_d)$ and labels $y = g(W x)$ with $W$ an $r$ x d matrix of rank r fixed as $d \\to \\infty$ and $g$ a fixed link function. For a standard two-layer network trained by online or multi-pass SGD on the square loss without data preprocessing, determine the exponent $\\gamma(g)$ in $n \\sim d^\\gamma$ required to reach test error $o(1)$, and determine whether it equals the benchmark for statistical-query and low-degree algorithms, $n \\sim d^{\\max(1, k_*/2)}$, with $k_*$ the generative exponent for single-index targets and the generative leap exponent for multi-index targets (Damian, Lee and Bruna, arXiv:2506.05500). The answer is $\\gamma$ as a function of the Hermite structure of $g$, with proof.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.long-range-interactions.dynamical-long-range-threshold",
      "fields": {
        "title": {
          "text": "Which power-law decays make interactions dynamically long-range?",
          "how": [
            "title:owner"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.mpemba-relaxation.markov-conditions",
      "fields": {
        "precise": {
          "text": "Continuous-time Markov jump process on n states with energies $E_i$ and barriers $B_{ij}$, Arrhenius rates $W_{ij} = \\exp(-(B_{ij} - E_j)/T_b)$ obeying detailed balance at bath temperature $T_b$, initial condition the Boltzmann distribution $\\pi(T_0)$. Expand $p(t) - \\pi(T_b) = \\sum_{k \\ge 2} a_k(T_0) v_k \\exp(-\\lambda_k t)$ with $0 < \\lambda_2 < \\lambda_3 \\le ...$; a weak direct Mpemba effect is $\\mid a_2(T_h)\\mid < \\mid a_2(T_c)\\mid$ for some $T_h > T_c > T_b$, a strong one is $a_2(T_h) = 0$, and an inverse effect is $\\mid a_2(T_c)\\mid < \\mid a_2(T_h)\\mid$ for some $T_c < T_h < T_b$. Find necessary and sufficient conditions on $\\{E_i, B_{ij}, T_b\\}$ for the weak and strong, direct and inverse effects, for general n, stated as explicit inequalities or sign conditions (for example on the graph of barriers) that do not require computing the eigenvectors of the generator.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.mpemba-relaxation.water-existence",
      "fields": {
        "title": {
          "text": "Does hot water reproducibly freeze before cold water?",
          "how": [
            "title:question-mark"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.nonequilibrium-steady-states.selection-principle-markov",
      "fields": {
        "precise": {
          "text": "For finite-state continuous-time Markov jump processes whose rates obey local detailed balance, $k(x\\to y)/k(y\\to x) = \\exp(s(x,y))$ with s the entropy flux to the environment, determine whether a variational functional built from entropy production and dynamical activity (frenesy, the time-symmetric part of the path weight) has an extremum that gives the stationary distribution to all orders in the driving, as minimum entropy production does to linear order. The Landauer blowtorch example shows stationary occupations depend on kinetic details beyond the entropy flux. Answer: yes with the functional and its domain, or a no-go theorem.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    },
    {
      "kind": "problem",
      "id": "stat.synchronization-networks.oscillator-glass",
      "fields": {
        "precise": {
          "text": "For dtheta_i/dt = $\\omega_i$ + sum_j $J_{ij}$ sin(theta_j - theta_i) with Gaussian omega_i of unit variance and symmetric Gaussian couplings J_ij of variance $J^2/N$ (the Daido model), determine whether for $J$ above some $J_g$ the $N \\to \\infty$ dynamics has a frozen component, for example a nonzero limit of $C(\\tau) = (1/2N) \\sum_i \\langle \\cos(\\theta_i(t+\\tau) - \\theta_i(t))\\rangle$ as $\\tau \\to \\infty$. The volcano transition near $J = 1.3$ (a change in shape of the local-field distribution) is established; its relation to a glass phase is the question. Answer: yes or no, with $J_g$.",
          "how": [
            "inside:operator-word"
          ]
        }
      }
    }
  ]
}