{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"880a2ae5140ba4f01171ba4d9249dffec0a0e34ae3ce43407998a29bd9b58ca2","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["51fdf35b7038f02ccd128e1c21a4dedb00fbbcef8baa723a04e3539d40fee0ba","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"3c48fabed4c98219eb3ad17d00a5804372d48f72c0a80d0bffa312a8c9e98bfe","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"cm.tc-limits.stiffness-bound-3d","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"In two-dimensional superconductors the transition temperature is provably limited by how stiff the superconducting phase is, which in turn is limited by how easily electrons move; whether a similar proof works in three dimensions is unknown.","posed_since":"2019","precise":"For two-dimensional superconductors the Berezinskii-Kosterlitz-Thouless relation and the optical sum rule give rigorous upper bounds on $T_c$ in terms of band dispersion and density (2019). Determine whether a comparable rigorous bound on $T_c$ exists in three dimensions, and in flat-band systems where the superfluid stiffness has a quantum-geometric contribution. An answer is a proof with stated assumptions or a counterexample model.","problem_ref":"51fdf35b7038f02ccd128e1c21a4dedb00fbbcef8baa723a04e3539d40fee0ba","references":"","settled_by":"A proof bounding $T_{c}$ by stiffness or kinetic-energy sum rules in 3D, or a solvable 3D model violating any such bound.","status_note":"","title":"Do superfluid-stiffness bounds on $T_c$ extend to three 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