{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3CTPS56RYFCYDOXQ2S6SO5SH4Y","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":"d65dd801ff3a18808ed87ca3a4b7091d2560739b5f96e33d8385fe82e9d5731c","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2024-10-24T12:13:41Z","title_canon_sha256":"e8cd234be75d600918b7c4cfa3912c47a2db29d5b1586b1a9a7ee20741d0a89d"},"schema_version":"1.0","source":{"id":"2410.18679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18679","created_at":"2026-07-05T09:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18679v1","created_at":"2026-07-05T09:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18679","created_at":"2026-07-05T09:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"3CTPS56RYFCY","created_at":"2026-07-05T09:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"3CTPS56RYFCYDOXQ","created_at":"2026-07-05T09:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"3CTPS56R","created_at":"2026-07-05T09:25:12Z"}],"graph_snapshots":[{"event_id":"sha256:6e1858db249ec615bc07c639d8731814ee7ff83283156d581a8405520ef0665d","target":"graph","created_at":"2026-07-05T09:25:12Z","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/2410.18679/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Superconductors are often discussed in the mean-field approximation that breaks $U(1)$ symmetry. Since the $U(1)$ symmetry underlies the charge conservation, naive application of response theory sometimes gives results that are not gauge-invariant. We study the effect of vertex corrections on the electromagnetic responses of superconductors by employing the gauge-invariant formulation, called consistent fluctuations of order parameters, that manifestly satisfy the Ward identity. For inversion broken two-band superconductors, we find that the linear and second-order optical responses are signif","authors_text":"Haruki Watanabe, Sena Watanabe","cross_cats":["cond-mat.stat-mech","cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2024-10-24T12:13:41Z","title":"A gauge-invariant formulation of optical responses in superconductors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18679","kind":"arxiv","version":1},"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":"sha256:2deb981802b5dcd8a83a406e0f40cbf806d3ffe38590345b8af7119a8393cc85","target":"record","created_at":"2026-07-05T09:25:12Z","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":"d65dd801ff3a18808ed87ca3a4b7091d2560739b5f96e33d8385fe82e9d5731c","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2024-10-24T12:13:41Z","title_canon_sha256":"e8cd234be75d600918b7c4cfa3912c47a2db29d5b1586b1a9a7ee20741d0a89d"},"schema_version":"1.0","source":{"id":"2410.18679","kind":"arxiv","version":1}},"canonical_sha256":"d8a6f977d1c14581baf0d4bd277647e63ba043e935f6680256efdce46cb1ffed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8a6f977d1c14581baf0d4bd277647e63ba043e935f6680256efdce46cb1ffed","first_computed_at":"2026-07-05T09:25:12.133249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:12.133249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A7Xwq+wiYqPztYp6wfBRj/aHB3GZvybaOSEm2eomN7oJv/P6SAp/Tyf9SPEohLJyldLO7DJ5YEx1+CD8IpgUBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:12.133711Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2deb981802b5dcd8a83a406e0f40cbf806d3ffe38590345b8af7119a8393cc85","sha256:6e1858db249ec615bc07c639d8731814ee7ff83283156d581a8405520ef0665d"],"state_sha256":"22c630fc2afd9d9748465e09b43abeb353af9ef1dece786336b49b850d1589bb"}