Location and origin of the sound-speed maximum in dense matter
In plain words
If sound in neutron-star matter first speeds up beyond the free-quark value and then slows down again, there must be a peak. Where the peak lies and what causes it, for example a gradual change from nucleons to quarks, is unknown.
Precise statement
Given $c_s^{2}(n) > c^{2}/3$ somewhere below the central density of a maximum-mass star, determine the density $n_{\mathrm{peak}}$ of the maximum of $c_s^{2}$ and its height, and the microscopic mechanism: quarkyonic matter (a phase with a quark Fermi sea surrounded by a shell of nucleons near the Fermi surface), a hadron-quark crossover, a first-order transition, or strongly repulsive hadronic interactions. Answer: $n_{\mathrm{peak}}/n_0$ and the maximum $c_s^{2}$ with uncertainties, plus a mechanism consistent with chiral EFT at low density and perturbative QCD at high density.
What would settle it
Equation-of-state inference using 2 percent radius measurements across 1.2 to 2.1 solar masses and post-merger gravitational-wave spectra, compared with model calculations of each mechanism.