{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JC6GMHFBWNOWHVZY5HLSO2QHKF","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":"9150aac383e40b9b0ad8c3290afdf11c42ac100dc904961099aa2189cc1d5b9e","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-04-09T13:20:28Z","title_canon_sha256":"40dbc907356cbc68b8ebdf39c538aab9661ef399cd92d37664c531ecf4257bec"},"schema_version":"1.0","source":{"id":"1504.02297","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02297","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02297v2","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02297","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"JC6GMHFBWNOW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JC6GMHFBWNOWHVZY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JC6GMHFB","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4c4570651522587460c56b245e5c636f7879dcb1a9d0005e91c9d690af14ca51","target":"graph","created_at":"2026-05-18T01:27:46Z","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":"We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes and globes, that enable the construction of free $\\omega$-categories on such objects. The excision of extremals is a recursive algorithm that presents every cell in such a category as a (unique) composite of atomic cells. This is the sense in which the $\\omega$-category is (freely) generated from its atoms. Due to the complicated multi-dimensional nature of","authors_text":"Mitchell Buckley","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-04-09T13:20:28Z","title":"Formalizing parity complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02297","kind":"arxiv","version":2},"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:a99bfcbd064c386c829661ff14dcc86c126d32a914aab90aa1f4f4053d40f384","target":"record","created_at":"2026-05-18T01:27:46Z","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":"9150aac383e40b9b0ad8c3290afdf11c42ac100dc904961099aa2189cc1d5b9e","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-04-09T13:20:28Z","title_canon_sha256":"40dbc907356cbc68b8ebdf39c538aab9661ef399cd92d37664c531ecf4257bec"},"schema_version":"1.0","source":{"id":"1504.02297","kind":"arxiv","version":2}},"canonical_sha256":"48bc661ca1b35d63d738e9d7276a0751638f6d87f4fb32a368e83e945f94fa14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48bc661ca1b35d63d738e9d7276a0751638f6d87f4fb32a368e83e945f94fa14","first_computed_at":"2026-05-18T01:27:46.170010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:46.170010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y8FHgFDMXy2oc+l6JM1wPf+lZ1htnwch1nPnWNqJynASS+RkquM5GjY1chXeKCGdrkMs/qnej+5Bs6ikSTJtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:46.170543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02297","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a99bfcbd064c386c829661ff14dcc86c126d32a914aab90aa1f4f4053d40f384","sha256:4c4570651522587460c56b245e5c636f7879dcb1a9d0005e91c9d690af14ca51"],"state_sha256":"554b7a952b570cbbb1f326d39c75cde8ee22f60f28a54d6b1dddd3bef3bc2799"}