{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C7HQHVYXBPYLB3RMZSXE673YR5","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":"01cfb9eacf7fc3c230ae05b8e02c98ba26443f67388d5fbdd85602c7a6fcffbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-04-11T10:39:58Z","title_canon_sha256":"d86186d480ca47fedbc482a04146a5993d2b41c3e82f783bd1b36ca10c8e7454"},"schema_version":"1.0","source":{"id":"1404.3067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3067","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3067v2","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3067","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"C7HQHVYXBPYL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C7HQHVYXBPYLB3RM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C7HQHVYX","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8368f8490cbc3b3d37fe06ce59fd8dc57dc648cb20f288d1d1a9126e5b80ed21","target":"graph","created_at":"2026-05-18T02:26:52Z","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 study the relation between Bourn's notion of peri-abelian category and conditions involving the coincidence of the Smith, Huq and Higgins commutators. In particular we show that a semi-abelian category is peri-abelian if and only if for each normal subobject $K\\leq X$, the Higgins commutator of $K$ with itself coincides with the normalisation of the Smith commutator of the denormalisation of $K$ with itself. We show that if a category is peri-abelian, then the condition (UCE), which was introduced and studied by Casas and the second author, holds for that category. In addition we show, usin","authors_text":"James R. A. Gray, Tim Van der Linden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-04-11T10:39:58Z","title":"Peri-abelian categories and the universal central extension condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3067","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":"sha256:90f561cdc8860c4fddfcf9c487146333718a3b663e4bc43a0124d5e146f2dbfb","target":"record","created_at":"2026-05-18T02:26:52Z","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":"01cfb9eacf7fc3c230ae05b8e02c98ba26443f67388d5fbdd85602c7a6fcffbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-04-11T10:39:58Z","title_canon_sha256":"d86186d480ca47fedbc482a04146a5993d2b41c3e82f783bd1b36ca10c8e7454"},"schema_version":"1.0","source":{"id":"1404.3067","kind":"arxiv","version":2}},"canonical_sha256":"17cf03d7170bf0b0ee2cccae4f7f788f6dd1a55b2d760a4b53a998f819d947cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17cf03d7170bf0b0ee2cccae4f7f788f6dd1a55b2d760a4b53a998f819d947cc","first_computed_at":"2026-05-18T02:26:52.921258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:52.921258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2ORzNfzNRIrjlk8Y5yjcocYA5aD1A8RnpM51Sap4bZqKCZy+h/0iKhO/FBMBHfElRH8Cz/ub9gUOKvV5szcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:52.921678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90f561cdc8860c4fddfcf9c487146333718a3b663e4bc43a0124d5e146f2dbfb","sha256:8368f8490cbc3b3d37fe06ce59fd8dc57dc648cb20f288d1d1a9126e5b80ed21"],"state_sha256":"26f9322bf7d20f58e4c3b2c53733827813cc57ce1c04d07f74864bd3b4ec4363"}