{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARY63B44E6NMJHQDJFTNEXKYCM","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":"815764f159b35cb5fdfc2557dff443028845af2407d1e8d1c98f224717bf1b2a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-04-12T02:20:01Z","title_canon_sha256":"f9cf41e1f2b1b7f833c83fdbece7630162644c0e3ac68ba7a05bc52ebb5c762a"},"schema_version":"1.0","source":{"id":"2604.10416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.10416","created_at":"2026-05-26T01:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"2604.10416v2","created_at":"2026-05-26T01:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.10416","created_at":"2026-05-26T01:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"ARY63B44E6NM","created_at":"2026-05-26T01:03:29Z"},{"alias_kind":"pith_short_16","alias_value":"ARY63B44E6NMJHQD","created_at":"2026-05-26T01:03:29Z"},{"alias_kind":"pith_short_8","alias_value":"ARY63B44","created_at":"2026-05-26T01:03:29Z"}],"graph_snapshots":[{"event_id":"sha256:6d2745f8f8e448a521e9fdb5bb8a88730a1841ca690cef892c6e650da1ca28f1","target":"graph","created_at":"2026-05-26T01:03:29Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact."}],"snapshot_sha256":"0be5eadcd9deb39691483a4c49bc6f5ebfebf595c5a682655ee6664a947d3066"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.10416/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Danhua Song","cross_cats":["math.MP"],"headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-04-12T02:20:01Z","title":"Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.10416","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T16:29:45.924742Z","id":"2dddd567-1d4b-4cbf-b740-9d71d21a804c","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","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.","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."}},"verdict_id":"2dddd567-1d4b-4cbf-b740-9d71d21a804c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3170415e09739921f96d786153a8bdfe5962ba140b22adad53af54e4c0ee23e8","target":"record","created_at":"2026-05-26T01:03:29Z","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":"815764f159b35cb5fdfc2557dff443028845af2407d1e8d1c98f224717bf1b2a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-04-12T02:20:01Z","title_canon_sha256":"f9cf41e1f2b1b7f833c83fdbece7630162644c0e3ac68ba7a05bc52ebb5c762a"},"schema_version":"1.0","source":{"id":"2604.10416","kind":"arxiv","version":2}},"canonical_sha256":"0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713","first_computed_at":"2026-05-26T01:03:29.866376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:29.866376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+4NENcWAX67ctbxrY/Gfm7SHs/2DLAPHeAE4SuYZqhxeeiKI/QpD9Bc3hyDrul9ijNNuxWhBTzKNfTRFdUkDg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:29.867171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.10416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3170415e09739921f96d786153a8bdfe5962ba140b22adad53af54e4c0ee23e8","sha256:6d2745f8f8e448a521e9fdb5bb8a88730a1841ca690cef892c6e650da1ca28f1"],"state_sha256":"4625ef75be4d084cdd00edf5cdc324343c75a22a522d7bfa045eddbca6d5f510"}