{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4ND3YZKFKUTAMB4PZUWBXFC5OH","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":"ddd4f32f569f54cf5c0704801d176c3b7a26da1e0c765c2d3dc3d63c29a62550","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-31T13:37:27Z","title_canon_sha256":"4d43b30d819ccf7cf39f23f94a170781104c400e2a347e21b4c1a46391c62602"},"schema_version":"1.0","source":{"id":"1810.13280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.13280","created_at":"2026-05-17T23:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.13280v1","created_at":"2026-05-17T23:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13280","created_at":"2026-05-17T23:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"4ND3YZKFKUTA","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4ND3YZKFKUTAMB4P","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4ND3YZKF","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:9aa35a1bbe7be7322584ff0cea6d9bf2317d61a40114e6e5e8bbdf0eba53812d","target":"graph","created_at":"2026-05-17T23:45:35Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The aim of this article is twofold: firstly, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual \\tch-de Rham construction; secondly, thanks to the above and still relying on a Heegaard splitting, we explain how to compute the partition functions of the $U(1)$ Chern-Simons and BF theories.","authors_text":"Frank Thuillier","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-31T13:37:27Z","title":"3D Topological Models and Heegaard Splitting I: Partition Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13280","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1a1a68710f82824744b0df4446665376487811c954e1b1395160edb599ed68e1","target":"record","created_at":"2026-05-17T23:45:35Z","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":"ddd4f32f569f54cf5c0704801d176c3b7a26da1e0c765c2d3dc3d63c29a62550","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-31T13:37:27Z","title_canon_sha256":"4d43b30d819ccf7cf39f23f94a170781104c400e2a347e21b4c1a46391c62602"},"schema_version":"1.0","source":{"id":"1810.13280","kind":"arxiv","version":1}},"canonical_sha256":"e347bc6545552606078fcd2c1b945d71ef379fea296549e9daec5a7be5654f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e347bc6545552606078fcd2c1b945d71ef379fea296549e9daec5a7be5654f7b","first_computed_at":"2026-05-17T23:45:35.652668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:35.652668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tKdOwSGPdgehoZnf5N4CZpD9Oawfya2hQ9H0fVkLz0xdu7EDMGHoVgqJPszemIq1kTjBEe+XgvWwPconaWlqCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:35.653546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.13280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1a68710f82824744b0df4446665376487811c954e1b1395160edb599ed68e1","sha256:9aa35a1bbe7be7322584ff0cea6d9bf2317d61a40114e6e5e8bbdf0eba53812d"],"state_sha256":"8bcb4e5d2e9191336f9105a33314a702661eff62d868f27baa1fbe49a184431c"}