{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TULB3DGCWRD6JRV6PO5Z3FLOYO","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":"11cab602a3775211dca4321e3c066aa29a8b20df51c20ad4e0b83602d5338aaf","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":"2025-01-23T14:55:19Z","title_canon_sha256":"9f86e0b433ae937147f84791688733fc1d07cec8c018660d3637cd4026a89d5b"},"schema_version":"1.0","source":{"id":"2501.13722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13722","created_at":"2026-07-05T11:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13722v2","created_at":"2026-07-05T11:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13722","created_at":"2026-07-05T11:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"TULB3DGCWRD6","created_at":"2026-07-05T11:03:55Z"},{"alias_kind":"pith_short_16","alias_value":"TULB3DGCWRD6JRV6","created_at":"2026-07-05T11:03:55Z"},{"alias_kind":"pith_short_8","alias_value":"TULB3DGC","created_at":"2026-07-05T11:03:55Z"}],"graph_snapshots":[{"event_id":"sha256:6f5a05da5ea24648e534432b1347baea78e53ba3112ffc67fb3c914b60c08f20","target":"graph","created_at":"2026-07-05T11:03:55Z","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/2501.13722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gauge invariance is essential for making physically meaningful predictions. In superconductors, mean-field Hamiltonians that explicitly break $U(1)$ symmetry often yield gauge-dependent results. While this issue has been resolved for linear responses in conventional superconductors, a unified framework that also covers unconventional superconductors and nonlinear responses has yet to be established. In this study, we present a comprehensive theoretical framework that enables gauge-invariant calculations of electromagnetic responses at arbitrary orders in external fields, applicable to both con","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":"2025-01-23T14:55:19Z","title":"Gauge-invariant electromagnetic responses in superconductors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13722","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:c6eff7be956ad45864fc8ddfbc89c41445beb910201f4e31252d212bafe7664e","target":"record","created_at":"2026-07-05T11:03:55Z","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":"11cab602a3775211dca4321e3c066aa29a8b20df51c20ad4e0b83602d5338aaf","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":"2025-01-23T14:55:19Z","title_canon_sha256":"9f86e0b433ae937147f84791688733fc1d07cec8c018660d3637cd4026a89d5b"},"schema_version":"1.0","source":{"id":"2501.13722","kind":"arxiv","version":2}},"canonical_sha256":"9d161d8cc2b447e4c6be7bbb9d956ec3bfbc4ed0e7fb27fdbb10eb209ef0cf92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d161d8cc2b447e4c6be7bbb9d956ec3bfbc4ed0e7fb27fdbb10eb209ef0cf92","first_computed_at":"2026-07-05T11:03:55.831137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:55.831137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvgvMTpa/IX3i5eB5JLhIKBtirLHdleXLB9cOww6Z4PHP0CTv9UumEk4H9xfEJ5d4OhpHgzwpCH/ix+HQ7QwBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:55.831635Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6eff7be956ad45864fc8ddfbc89c41445beb910201f4e31252d212bafe7664e","sha256:6f5a05da5ea24648e534432b1347baea78e53ba3112ffc67fb3c914b60c08f20"],"state_sha256":"c0a9543f2a82b1fc5e6eec93abbd3d4ea1d687145ace413461038fb9c2582522"}