{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4SBART2ZTTOG22QLQ3OHWTEUIO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"129ee6c9ffba7bdd5cd3d6a913327dd934a1cfbba898c11354dde2a1b22539c8","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-25T19:16:40Z","title_canon_sha256":"4d3991617993239be1725eb43ce1b366cd26f253c82430f3634185fcc5f61afb"},"schema_version":"1.0","source":{"id":"2409.17297","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.17297","created_at":"2026-07-05T09:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"2409.17297v2","created_at":"2026-07-05T09:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.17297","created_at":"2026-07-05T09:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"4SBART2ZTTOG","created_at":"2026-07-05T09:23:12Z"},{"alias_kind":"pith_short_16","alias_value":"4SBART2ZTTOG22QL","created_at":"2026-07-05T09:23:12Z"},{"alias_kind":"pith_short_8","alias_value":"4SBART2Z","created_at":"2026-07-05T09:23:12Z"}],"graph_snapshots":[{"event_id":"sha256:4a04839e54a757b94f48a43c6ed7e24c49131002e4fa59cedb08ecfe9e9634c0","target":"graph","created_at":"2026-07-05T09:23:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.17297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a multi-band BCS free energy functional and prove that for a multi-band superconductor the effect of inter-band coupling can only increase the critical temperature, irrespective of its attractive or repulsive nature and its strength. Further, for weak coupling and weaker inter-band coupling, we prove that the dependence of the increase in critical temperature on the inter-band coupling is (1) linear, if there are two or more equally strongly superconducting bands, or (2) quadratic, if there is only one dominating band.","authors_text":"Asbj{\\o}rn B{\\ae}kgaard Lauritsen, Edwin Langmann, Joscha Henheik","cross_cats":["cond-mat.quant-gas","cond-mat.supr-con","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-25T19:16:40Z","title":"Multi-band superconductors have enhanced critical temperatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17297","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8002eb72d3a19899d50a2e12d7a4e4d70cb4412ec3939e18f73ed402c323ebba","target":"record","created_at":"2026-07-05T09:23:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"129ee6c9ffba7bdd5cd3d6a913327dd934a1cfbba898c11354dde2a1b22539c8","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-25T19:16:40Z","title_canon_sha256":"4d3991617993239be1725eb43ce1b366cd26f253c82430f3634185fcc5f61afb"},"schema_version":"1.0","source":{"id":"2409.17297","kind":"arxiv","version":2}},"canonical_sha256":"e48208cf599cdc6d6a0b86dc7b4c94438ce8fa81413cb9fcbfbac86e1acb7413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e48208cf599cdc6d6a0b86dc7b4c94438ce8fa81413cb9fcbfbac86e1acb7413","first_computed_at":"2026-07-05T09:23:12.783403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:12.783403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcU20XFekNyool1X4BGadU3bvyNRVY1jxa0yb4SqO09Mheo90KKvatdMNVgrqXVZH5QDNZWko8gM/kqYgyxSCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:12.783876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.17297","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8002eb72d3a19899d50a2e12d7a4e4d70cb4412ec3939e18f73ed402c323ebba","sha256:4a04839e54a757b94f48a43c6ed7e24c49131002e4fa59cedb08ecfe9e9634c0"],"state_sha256":"26c7916f85ef56c879a2c6577380eca670d7aeda872ecf1a96a9bf37def612bc"}