{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XMQCE4BQD74WW4UKE45LJ7MYPY","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":"0b4f5e5127eb953119e5bb1c90244419d3e80147ef274b6bfc40bfcaec90fc03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-07T07:44:39Z","title_canon_sha256":"f2771d4ba363f5e38611b09128a951297e6cfbb1198d9658db7f32ff3f45a92d"},"schema_version":"1.0","source":{"id":"1803.03137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03137","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03137v1","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03137","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"XMQCE4BQD74W","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XMQCE4BQD74WW4UK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XMQCE4BQ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:4f88d565066b34fcfbe026b4e0c678c417faca588334e54e8ff2048645e371ea","target":"graph","created_at":"2026-05-18T00:21:44Z","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":"In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute the biquandle cocycle invariants from marked graph diagrams. We also develop the shadow (co)homology theory of biquandles and construct the shadow biquandle cocycle invariants for oriented surface-links.","authors_text":"Akio Kawauchi, Jieon Kim, Sang Youl Lee, Seiichi Kamada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-07T07:44:39Z","title":"Biquandle cohomology and state-sum invariants of links and surface-links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03137","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":"sha256:293025aeb3c8d6fd638f1008331047c08d2d6dbbf5b43637d051c700cdfb1757","target":"record","created_at":"2026-05-18T00:21:44Z","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":"0b4f5e5127eb953119e5bb1c90244419d3e80147ef274b6bfc40bfcaec90fc03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-07T07:44:39Z","title_canon_sha256":"f2771d4ba363f5e38611b09128a951297e6cfbb1198d9658db7f32ff3f45a92d"},"schema_version":"1.0","source":{"id":"1803.03137","kind":"arxiv","version":1}},"canonical_sha256":"bb202270301ff96b728a273ab4fd987e07b3ac2e02793c68cc0b09e2d74174f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb202270301ff96b728a273ab4fd987e07b3ac2e02793c68cc0b09e2d74174f6","first_computed_at":"2026-05-18T00:21:44.344295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:44.344295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dHKurW5tI/pgfrmRfcDK9KLXs1Lm8XrHNNxLVs5wwjYlceeQslX1e8EF2ZHV68bwjW6nYs/RF92qdq7ZajNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:44.344980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293025aeb3c8d6fd638f1008331047c08d2d6dbbf5b43637d051c700cdfb1757","sha256:4f88d565066b34fcfbe026b4e0c678c417faca588334e54e8ff2048645e371ea"],"state_sha256":"8f8775076ffec6fbd49209f127d8eadba4babb796778bdd634426677dbe60f09"}