{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:46Q3RJ7FJSUWEQHHHPNSKMIH5M","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":"c30b77a8e54b36863da1a287661555c0f97b039888b438195dddad8c52d4612b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-25T11:59:44Z","title_canon_sha256":"d2cd68379cb929b29d9e56f1f4a22747aca72e1335853cdcd9d27f0f807f08f4"},"schema_version":"1.0","source":{"id":"1304.6883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6883","created_at":"2026-05-18T03:16:05Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6883v2","created_at":"2026-05-18T03:16:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6883","created_at":"2026-05-18T03:16:05Z"},{"alias_kind":"pith_short_12","alias_value":"46Q3RJ7FJSUW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46Q3RJ7FJSUWEQHH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46Q3RJ7F","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:2c68aaaa13c03402a7478fe1e27c151e618f006ced3f5ea4bf414b3fc4d15067","target":"graph","created_at":"2026-05-18T03:16:05Z","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 propose the notion of association schemoids generalizing that of association schemes from small categorical points of view. In particular, a generalization of the Bose-Mesner algebra of an association scheme appears as a subalgebra in the category algebra of the underlying category of a schemoid. In this paper, the equivalence between the categories of grouopids and that of thin association schemoids is established. Moreover linear extensions of schemoids are considered. A general theory of the Baues-Wirsching cohomology deduces a classification theorem for such extensions of a schemoid. We","authors_text":"Katsuhiko Kuribayashi, Kentaro Matsuo","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-25T11:59:44Z","title":"Association schemoids and their categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6883","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":"sha256:177b99c4dea8ee09128ccdd5f05c1259202fe78811f1896ac5f51136ffd20842","target":"record","created_at":"2026-05-18T03:16:05Z","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":"c30b77a8e54b36863da1a287661555c0f97b039888b438195dddad8c52d4612b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-25T11:59:44Z","title_canon_sha256":"d2cd68379cb929b29d9e56f1f4a22747aca72e1335853cdcd9d27f0f807f08f4"},"schema_version":"1.0","source":{"id":"1304.6883","kind":"arxiv","version":2}},"canonical_sha256":"e7a1b8a7e54ca96240e73bdb253107eb316dd45a89d768a2be4a00b765206c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a1b8a7e54ca96240e73bdb253107eb316dd45a89d768a2be4a00b765206c0a","first_computed_at":"2026-05-18T03:16:05.964468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:05.964468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFYrobRD2IMZEdHnT0HJb9LS23my1vVPP7vDISbCD4hygdWulhQ7X5BWWl2o4afPHlygn/kl3iSxv2yWtBFHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:05.965059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:177b99c4dea8ee09128ccdd5f05c1259202fe78811f1896ac5f51136ffd20842","sha256:2c68aaaa13c03402a7478fe1e27c151e618f006ced3f5ea4bf414b3fc4d15067"],"state_sha256":"1e20c8ed476de92f25bda768e8d4ec5ffc45f9d974f8d7b03b7eb61a5ca1e5c6"}