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Standard theory gives no reliable prediction at such low density with such light carriers.","posed_since":"2017","precise":"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.","problem_ref":"c06b43052b569089ee2eb54d2f8ab4c94a606c214ded19648eea642882c7a4f6","references":"","settled_by":"A non-adiabatic pairing calculation reproducing $0.53\\,\\mathrm{mK}$ and the measured critical field, tested by the isotope or pressure dependence of $T_{c}$.","status_note":"","title":"How semimetallic bismuth superconducts at half a 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