{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"bd105edc5b2019ebdcd7fc6942000655ec51f49912a5e92f4a9703e6b9afc281","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b57e68af071e079c183d6922a3394bf1cdf1415d7a1ec673279c4930d5d8b401","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":"1","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":null,"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 dimensions","topic_ref":"b4b75ff0c70cf5671429b9fb89c50704ada0cab4ee0e1be6e0ee986b669f9fe8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"51fdf35b7038f02ccd128e1c21a4dedb00fbbcef8baa723a04e3539d40fee0ba","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"52dc7bdd91de7d705711508a272a7c1937a6033eb2dfac703931f86aeb0909d9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"tNbyavemZU6VK23hfe5DFA351UtsZ4b0bhOjehFzqLYFOeGk98xBqr3HXBee87rSLQF1Toq2dGlhNwy2NeJAAg"},"schema":"pubphys.envelope/1"},"record_hash":"51fdf35b7038f02ccd128e1c21a4dedb00fbbcef8baa723a04e3539d40fee0ba","leaf_index":1192}