{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ARY63B44E6NMJHQDJFTNEXKYCM","short_pith_number":"pith:ARY63B44","schema_version":"1.0","canonical_sha256":"0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713","source":{"kind":"arxiv","id":"2604.10416","version":2},"attestation_state":"computed","paper":{"title":"Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Danhua Song","submitted_at":"2026-04-12T02:20:01Z","abstract_excerpt":"We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the $(2n+2)$-dimensional higher CS forms and transgression forms for strict Lie 2-groups presented by Lie crossed modules. Given two 2-connections related by a higher gauge transformation, higher transgression forms yield canonical higher WZW and gWZW terms. We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas t"},"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":"2604.10416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-04-12T02:20:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f9cf41e1f2b1b7f833c83fdbece7630162644c0e3ac68ba7a05bc52ebb5c762a","abstract_canon_sha256":"815764f159b35cb5fdfc2557dff443028845af2407d1e8d1c98f224717bf1b2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:29.867171Z","signature_b64":"B+4NENcWAX67ctbxrY/Gfm7SHs/2DLAPHeAE4SuYZqhxeeiKI/QpD9Bc3hyDrul9ijNNuxWhBTzKNfTRFdUkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713","last_reissued_at":"2026-05-26T01:03:29.866376Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:29.866376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Danhua Song","submitted_at":"2026-04-12T02:20:01Z","abstract_excerpt":"We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the $(2n+2)$-dimensional higher CS forms and transgression forms for strict Lie 2-groups presented by Lie crossed modules. Given two 2-connections related by a higher gauge transformation, higher transgression forms yield canonical higher WZW and gWZW terms. We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derivation assumes that strict Lie 2-groups are presented by Lie crossed modules and that a symmetric invariant polynomial exists for the associated differential crossed modules, allowing the Cartan homotopy formula to produce the required transgression forms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Higher WZW terms vanish and gauged versions are exact for symmetric invariant polynomials on differential crossed modules, making higher CS actions gauge-invariant on closed manifolds with boundary dependence isolated.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0be5eadcd9deb39691483a4c49bc6f5ebfebf595c5a682655ee6664a947d3066"},"source":{"id":"2604.10416","kind":"arxiv","version":2},"verdict":{"id":"2dddd567-1d4b-4cbf-b740-9d71d21a804c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:29:45.924742Z","strongest_claim":"We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.","one_line_summary":"Higher WZW terms vanish and gauged versions are exact for symmetric invariant polynomials on differential crossed modules, making higher CS actions gauge-invariant on closed manifolds with boundary dependence isolated.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derivation assumes that strict Lie 2-groups are presented by Lie crossed modules and that a symmetric invariant polynomial exists for the associated differential crossed modules, allowing the Cartan homotopy formula to produce the required transgression forms.","pith_extraction_headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10416/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":"2604.10416","created_at":"2026-05-26T01:03:29.866499+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.10416v2","created_at":"2026-05-26T01:03:29.866499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.10416","created_at":"2026-05-26T01:03:29.866499+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARY63B44E6NM","created_at":"2026-05-26T01:03:29.866499+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARY63B44E6NMJHQD","created_at":"2026-05-26T01:03:29.866499+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARY63B44","created_at":"2026-05-26T01:03:29.866499+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/ARY63B44E6NMJHQDJFTNEXKYCM","json":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM.json","graph_json":"https://pith.science/api/pith-number/ARY63B44E6NMJHQDJFTNEXKYCM/graph.json","events_json":"https://pith.science/api/pith-number/ARY63B44E6NMJHQDJFTNEXKYCM/events.json","paper":"https://pith.science/paper/ARY63B44"},"agent_actions":{"view_html":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM","download_json":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM.json","view_paper":"https://pith.science/paper/ARY63B44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.10416&json=true","fetch_graph":"https://pith.science/api/pith-number/ARY63B44E6NMJHQDJFTNEXKYCM/graph.json","fetch_events":"https://pith.science/api/pith-number/ARY63B44E6NMJHQDJFTNEXKYCM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM/action/storage_attestation","attest_author":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM/action/author_attestation","sign_citation":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM/action/citation_signature","submit_replication":"https://pith.science/pith/ARY63B44E6NMJHQDJFTNEXKYCM/action/replication_record"}},"created_at":"2026-05-26T01:03:29.866499+00:00","updated_at":"2026-05-26T01:03:29.866499+00:00"}