{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:X3LPLBNCWIYWU4TO2AOFJZYU4K","short_pith_number":"pith:X3LPLBNC","schema_version":"1.0","canonical_sha256":"bed6f585a2b2316a726ed01c54e714e286b499e728c88b8b479d8e8d61e3f8ab","source":{"kind":"arxiv","id":"2009.07621","version":2},"attestation_state":"computed","paper":{"title":"Topological mass generation in gapless systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-ph"],"primary_cat":"hep-th","authors_text":"Naoki Yamamoto, Ryo Yokokura","submitted_at":"2020-09-16T11:59:52Z","abstract_excerpt":"Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$ dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These systems also exhibit the spontaneous breaking of higher-form $\\mathbb{Z}_k$ symmetries and topological orders for level $k \\geq 2$. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level $k$ in $(3+1)$ dimensions in background fields that hosts both gapped and gapless modes. We argu"},"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":"2009.07621","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-16T11:59:52Z","cross_cats_sorted":["cond-mat.mes-hall","hep-ph"],"title_canon_sha256":"c61e104bd5823c873a75ffc82861cacbd1474ee4b3ba263455cee53e6a08565f","abstract_canon_sha256":"e0482253bec64fce7fd5d91c7b659e2a4239b3d795416689c24f6b217f42f71c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:57:50.244231Z","signature_b64":"nn/l6mvFWywd7kNWAXfI0l3SKrcsB0JqBxGA0vxl+4HcYBfvv8ROd3ff10TqEdgEjOhMzvs+t//9Sws41sNwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bed6f585a2b2316a726ed01c54e714e286b499e728c88b8b479d8e8d61e3f8ab","last_reissued_at":"2026-07-05T02:57:50.243806Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:57:50.243806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological mass generation in gapless systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-ph"],"primary_cat":"hep-th","authors_text":"Naoki Yamamoto, Ryo Yokokura","submitted_at":"2020-09-16T11:59:52Z","abstract_excerpt":"Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$ dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These systems also exhibit the spontaneous breaking of higher-form $\\mathbb{Z}_k$ symmetries and topological orders for level $k \\geq 2$. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level $k$ in $(3+1)$ dimensions in background fields that hosts both gapped and gapless modes. We argu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07621","kind":"arxiv","version":2},"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/2009.07621/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":"2009.07621","created_at":"2026-07-05T02:57:50.243864+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.07621v2","created_at":"2026-07-05T02:57:50.243864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07621","created_at":"2026-07-05T02:57:50.243864+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3LPLBNCWIYW","created_at":"2026-07-05T02:57:50.243864+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3LPLBNCWIYWU4TO","created_at":"2026-07-05T02:57:50.243864+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3LPLBNC","created_at":"2026-07-05T02:57:50.243864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K","json":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K.json","graph_json":"https://pith.science/api/pith-number/X3LPLBNCWIYWU4TO2AOFJZYU4K/graph.json","events_json":"https://pith.science/api/pith-number/X3LPLBNCWIYWU4TO2AOFJZYU4K/events.json","paper":"https://pith.science/paper/X3LPLBNC"},"agent_actions":{"view_html":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K","download_json":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K.json","view_paper":"https://pith.science/paper/X3LPLBNC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.07621&json=true","fetch_graph":"https://pith.science/api/pith-number/X3LPLBNCWIYWU4TO2AOFJZYU4K/graph.json","fetch_events":"https://pith.science/api/pith-number/X3LPLBNCWIYWU4TO2AOFJZYU4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K/action/storage_attestation","attest_author":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K/action/author_attestation","sign_citation":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K/action/citation_signature","submit_replication":"https://pith.science/pith/X3LPLBNCWIYWU4TO2AOFJZYU4K/action/replication_record"}},"created_at":"2026-07-05T02:57:50.243864+00:00","updated_at":"2026-07-05T02:57:50.243864+00:00"}