{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:LTM46PSPLNJMOIPKOYYQKY7KZW","short_pith_number":"pith:LTM46PSP","schema_version":"1.0","canonical_sha256":"5cd9cf3e4f5b52c721ea76310563eacd832a09ed7f24c0ddfdca7789d9a616d2","source":{"kind":"arxiv","id":"2303.08136","version":1},"attestation_state":"computed","paper":{"title":"Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.supr-con","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Ashvin Vishwanath, Ruben Verresen, Ryan Thorngren, Tibor Rakovszky","submitted_at":"2023-03-14T17:59:42Z","abstract_excerpt":"Classifying Higgs phases within the landscape of gapped and symmetry preserving states of matter presents a conceptual challenge. We argue that $U(1)$ Higgs phases are symmetry-protected topological (SPT) phases and we derive their topological response theory and boundary anomaly -- applicable to superconductors treated with dynamical electromagnetic field. This generalizes the discussion of discrete gauge theories by Verresen et al., arXiv:2211.01376. We show that a Higgs phase in $d$ spatial dimensions is in a non-trivial SPT class protected by a global $U(1)$ symmetry associated with the Hi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2303.08136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2023-03-14T17:59:42Z","cross_cats_sorted":["cond-mat.supr-con","hep-th","quant-ph"],"title_canon_sha256":"5f6e368aa0ed225ec40cbfd42ff2b77f0d1d96e096f9f0d47862eddd13c7a283","abstract_canon_sha256":"67c6a45f9092bd7ecfdfdebc3f5b712a6eb94a3b30e3798950ece990cd395147"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:15.176181Z","signature_b64":"ddW5V6OvjfhGUFwDXJNjbvCTyLYxrELaBmJSg3Q2jToWbvzPyYQAJPdAV0mGU4T/QX+jJutwisaoy2PSxeQdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd9cf3e4f5b52c721ea76310563eacd832a09ed7f24c0ddfdca7789d9a616d2","last_reissued_at":"2026-07-05T05:51:15.175638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:15.175638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.supr-con","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Ashvin Vishwanath, Ruben Verresen, Ryan Thorngren, Tibor Rakovszky","submitted_at":"2023-03-14T17:59:42Z","abstract_excerpt":"Classifying Higgs phases within the landscape of gapped and symmetry preserving states of matter presents a conceptual challenge. We argue that $U(1)$ Higgs phases are symmetry-protected topological (SPT) phases and we derive their topological response theory and boundary anomaly -- applicable to superconductors treated with dynamical electromagnetic field. This generalizes the discussion of discrete gauge theories by Verresen et al., arXiv:2211.01376. We show that a Higgs phase in $d$ spatial dimensions is in a non-trivial SPT class protected by a global $U(1)$ symmetry associated with the Hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.08136","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.08136/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2303.08136","created_at":"2026-07-05T05:51:15.175708+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.08136v1","created_at":"2026-07-05T05:51:15.175708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.08136","created_at":"2026-07-05T05:51:15.175708+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTM46PSPLNJM","created_at":"2026-07-05T05:51:15.175708+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTM46PSPLNJMOIPK","created_at":"2026-07-05T05:51:15.175708+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTM46PSP","created_at":"2026-07-05T05:51:15.175708+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2509.20054","citing_title":"Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2509.09587","citing_title":"PT symmetry-enriched non-unitary criticality","ref_index":100,"is_internal_anchor":false},{"citing_arxiv_id":"2509.20054","citing_title":"Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2604.01166","citing_title":"Varieties of electrically charged physical states in SU(2)$\\times$U(1) lattice gauge Higgs theory","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18733","citing_title":"Gauging in superconductors and other electronic systems","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW","json":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW.json","graph_json":"https://pith.science/api/pith-number/LTM46PSPLNJMOIPKOYYQKY7KZW/graph.json","events_json":"https://pith.science/api/pith-number/LTM46PSPLNJMOIPKOYYQKY7KZW/events.json","paper":"https://pith.science/paper/LTM46PSP"},"agent_actions":{"view_html":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW","download_json":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW.json","view_paper":"https://pith.science/paper/LTM46PSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.08136&json=true","fetch_graph":"https://pith.science/api/pith-number/LTM46PSPLNJMOIPKOYYQKY7KZW/graph.json","fetch_events":"https://pith.science/api/pith-number/LTM46PSPLNJMOIPKOYYQKY7KZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW/action/storage_attestation","attest_author":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW/action/author_attestation","sign_citation":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW/action/citation_signature","submit_replication":"https://pith.science/pith/LTM46PSPLNJMOIPKOYYQKY7KZW/action/replication_record"}},"created_at":"2026-07-05T05:51:15.175708+00:00","updated_at":"2026-07-05T05:51:15.175708+00:00"}