{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IFRWXZV3WP2BUX2JRBNBUPUHKA","short_pith_number":"pith:IFRWXZV3","schema_version":"1.0","canonical_sha256":"41636be6bbb3f41a5f49885a1a3e8750240b0a91d12b1bbb47cdbce2315360b4","source":{"kind":"arxiv","id":"1703.03266","version":5},"attestation_state":"computed","paper":{"title":"Explicit cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf-Witten invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AT","authors_text":"Hua-Lin Huang, Yu Ye, Zheyan Wan","submitted_at":"2017-03-09T14:15:56Z","abstract_excerpt":"We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf-Witten Invariants of the $n$-torus for all $n$."},"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":"1703.03266","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-09T14:15:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5bfd08c5b9d629640e557823aac1431c8f0e81fcd6af7a216b0d8c53f07ab6af","abstract_canon_sha256":"9dd56b64d57281702d692a5adac73cde5b7685d689bb46433877e168f8656195"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:28.911131Z","signature_b64":"P+EbFub/QOADGugGQjO5FQdktbz0vVdUM3wzxtjw4rejEYlvHNgHZjQyZgtg5iNuBPi1fVIM2XQrAMpvmKd1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41636be6bbb3f41a5f49885a1a3e8750240b0a91d12b1bbb47cdbce2315360b4","last_reissued_at":"2026-05-17T23:50:28.910520Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:28.910520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf-Witten invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AT","authors_text":"Hua-Lin Huang, Yu Ye, Zheyan Wan","submitted_at":"2017-03-09T14:15:56Z","abstract_excerpt":"We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf-Witten Invariants of the $n$-torus for all $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03266","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1703.03266","created_at":"2026-05-17T23:50:28.910629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03266v5","created_at":"2026-05-17T23:50:28.910629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03266","created_at":"2026-05-17T23:50:28.910629+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFRWXZV3WP2B","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFRWXZV3WP2BUX2J","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFRWXZV3","created_at":"2026-05-18T12:31:21.493067+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/IFRWXZV3WP2BUX2JRBNBUPUHKA","json":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA.json","graph_json":"https://pith.science/api/pith-number/IFRWXZV3WP2BUX2JRBNBUPUHKA/graph.json","events_json":"https://pith.science/api/pith-number/IFRWXZV3WP2BUX2JRBNBUPUHKA/events.json","paper":"https://pith.science/paper/IFRWXZV3"},"agent_actions":{"view_html":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA","download_json":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA.json","view_paper":"https://pith.science/paper/IFRWXZV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03266&json=true","fetch_graph":"https://pith.science/api/pith-number/IFRWXZV3WP2BUX2JRBNBUPUHKA/graph.json","fetch_events":"https://pith.science/api/pith-number/IFRWXZV3WP2BUX2JRBNBUPUHKA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA/action/storage_attestation","attest_author":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA/action/author_attestation","sign_citation":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA/action/citation_signature","submit_replication":"https://pith.science/pith/IFRWXZV3WP2BUX2JRBNBUPUHKA/action/replication_record"}},"created_at":"2026-05-17T23:50:28.910629+00:00","updated_at":"2026-05-17T23:50:28.910629+00:00"}