{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OOYP7F5SZABT3YT4NUN6SJIBYO","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":"df842ba5df639c0e58a97efd0aaccee85b980462db1e8578ddf1baf8b67a3ac9","cross_cats_sorted":["hep-lat","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2019-05-22T23:39:49Z","title_canon_sha256":"72fd9782ce1d3e73ece189a0150f216104dc2d5b85be844921518d5e19e28057"},"schema_version":"1.0","source":{"id":"1905.09406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09406","created_at":"2026-07-05T00:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09406v2","created_at":"2026-07-05T00:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09406","created_at":"2026-07-05T00:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"OOYP7F5SZABT","created_at":"2026-07-05T00:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"OOYP7F5SZABT3YT4","created_at":"2026-07-05T00:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"OOYP7F5S","created_at":"2026-07-05T00:21:58Z"}],"graph_snapshots":[{"event_id":"sha256:9ec780b1a8fb1fce9275e13c3b979c2f9a67eccfb5e0a5a9ef96d308b408a93d","target":"graph","created_at":"2026-07-05T00:21:58Z","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/1905.09406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global subgroup of the local U(1) gauge symmetry may be regarded, in analogy to non-abelian theories, as a \"custodial\" symmetry affecting the matter field alone, and construct, along the lines of our previous work, a new gauge-invariant criterion for breaking symmetries of this kind. It is shown that spontaneous breaking of custodial symmetry is a necessary condition f","authors_text":"Jeff Greensite, Kazue Matsuyama","cross_cats":["hep-lat","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2019-05-22T23:39:49Z","title":"The nature of symmetry breaking in the superconducting ground state"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09406","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:eb8cdda072901bb1b7d05eb95f2c589fb6a9f6de0552c2e65ed0583a7d46c66e","target":"record","created_at":"2026-07-05T00:21:58Z","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":"df842ba5df639c0e58a97efd0aaccee85b980462db1e8578ddf1baf8b67a3ac9","cross_cats_sorted":["hep-lat","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2019-05-22T23:39:49Z","title_canon_sha256":"72fd9782ce1d3e73ece189a0150f216104dc2d5b85be844921518d5e19e28057"},"schema_version":"1.0","source":{"id":"1905.09406","kind":"arxiv","version":2}},"canonical_sha256":"73b0ff97b2c8033de27c6d1be92501c3b2f6c43927e3bb5a65e0998311ef6876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73b0ff97b2c8033de27c6d1be92501c3b2f6c43927e3bb5a65e0998311ef6876","first_computed_at":"2026-07-05T00:21:58.031741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:21:58.031741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txH7Z26G/6mrCuudSHLWyfv6YccJblWtx5LLPFlLHH82ZBF2PqotYSAzKMJ0I6tzaEZeoHAenoPOtFBcA5pMAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:21:58.032094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8cdda072901bb1b7d05eb95f2c589fb6a9f6de0552c2e65ed0583a7d46c66e","sha256:9ec780b1a8fb1fce9275e13c3b979c2f9a67eccfb5e0a5a9ef96d308b408a93d"],"state_sha256":"a8d4cfc343bcf0520c9a664404c6535cbacc6286132fa4c11d550b7ffedd85d9"}