{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YRFMP4EM22MH6SR6E5G5ZW32WN","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":"1c1de10dd996e200b7474e70bb30911dac3bdcd1660e74cb6b0517a1871dd30b","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-16T16:51:23Z","title_canon_sha256":"1b23a6eaf1176b9db4fa3ab14949f517c93f1908d0157d10b65e99d896476e79"},"schema_version":"1.0","source":{"id":"1012.3672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3672","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3672v1","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3672","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"YRFMP4EM22MH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YRFMP4EM22MH6SR6","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YRFMP4EM","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:5c57d59261271f8f4d3a79c97cb5350177e14396d51ebb4e710b451610f1e654","target":"graph","created_at":"2026-05-18T02:41:50Z","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 SO(3) Kauffman polynomial and the chromatic polynomial of planar graphs are categorified by a unique extension of the Khovanov homology framework. Many structural observations and computations of homologies of knots and spin networks are included.","authors_text":"Benjamin Cooper, Matt Hogancamp, Vyacheslav Krushkal","cross_cats":["math.CO","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-16T16:51:23Z","title":"SO(3) Homology of Graphs and Links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3672","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":"sha256:588fb143a6854547fcc103a3abe3f3128eef831543521f4ee13058d05be2b5d5","target":"record","created_at":"2026-05-18T02:41:50Z","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":"1c1de10dd996e200b7474e70bb30911dac3bdcd1660e74cb6b0517a1871dd30b","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-16T16:51:23Z","title_canon_sha256":"1b23a6eaf1176b9db4fa3ab14949f517c93f1908d0157d10b65e99d896476e79"},"schema_version":"1.0","source":{"id":"1012.3672","kind":"arxiv","version":1}},"canonical_sha256":"c44ac7f08cd6987f4a3e274ddcdb7ab350f3d2af03a0907be94236cb16310d58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c44ac7f08cd6987f4a3e274ddcdb7ab350f3d2af03a0907be94236cb16310d58","first_computed_at":"2026-05-18T02:41:50.622026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:50.622026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Z8gJTc4RYbJmc5B+7NdZaXuT4E7pneOb/VVepGp+ILfwAE9W3WLXjezVzpnpJciBSda8A6Vh0uRgOUZvHnsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:50.622530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:588fb143a6854547fcc103a3abe3f3128eef831543521f4ee13058d05be2b5d5","sha256:5c57d59261271f8f4d3a79c97cb5350177e14396d51ebb4e710b451610f1e654"],"state_sha256":"2073151b51e17800935c05b241b479ce83dc73aae4e8eafec8cd14010b0936aa"}