{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VTKAB65NFRAIGT4X6ADV4UFLR3","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":"f9d867d1173802736fa1fc49a2a1d2ad30c679fa756e56c8294eb3880997a3ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-12-17T12:50:25Z","title_canon_sha256":"d26e666adbfe045be1ba1064a4ab30c613a528c74fb95eaef14cafe614712b19"},"schema_version":"1.0","source":{"id":"1012.3870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3870","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3870v2","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3870","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"VTKAB65NFRAI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VTKAB65NFRAIGT4X","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VTKAB65N","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:bff83a5e5802d1f5b8740acf516d76c4c20eca0ef1c692ae0a49e5266af2061b","target":"graph","created_at":"2026-05-18T04:19:32Z","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":"Each small site (C,J) determines a small quantaloid of closed cribles R(C,J). We prove that a small quantaloid Q is equivalent to R(C,J) for some small site (C,J) if and only if there exists a (necessarily subcanonical) Grothendieck topology J on the category Map(Q) of left adjoints in Q such that Q=R(Map(Q),J), if and only if Q is locally localic, map- discrete, weakly tabular and weakly modular. If moreover coreflexives split in Q, then the topology J on Map(Q) is the canonical topology.","authors_text":"Hans Heymans, Isar Stubbe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-12-17T12:50:25Z","title":"Elementary characterisation of small quantaloids of closed cribles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3870","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:d112e20d822dbc39a1eaca04d1a233545d2e01941458c4c1c2439e2e356c722b","target":"record","created_at":"2026-05-18T04:19:32Z","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":"f9d867d1173802736fa1fc49a2a1d2ad30c679fa756e56c8294eb3880997a3ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-12-17T12:50:25Z","title_canon_sha256":"d26e666adbfe045be1ba1064a4ab30c613a528c74fb95eaef14cafe614712b19"},"schema_version":"1.0","source":{"id":"1012.3870","kind":"arxiv","version":2}},"canonical_sha256":"acd400fbad2c40834f97f0075e50ab8ef67406fcd287e0da6c9705ee83e8f3f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd400fbad2c40834f97f0075e50ab8ef67406fcd287e0da6c9705ee83e8f3f8","first_computed_at":"2026-05-18T04:19:32.148794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:32.148794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"71kjrHPHWinMJgcEjZQI6THKZ+iJ4V0W9DwUQsG5/GKTmG7w9ybfynzJuCZbj+83leKhlINCt4AHtiPtWCGiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:32.149174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d112e20d822dbc39a1eaca04d1a233545d2e01941458c4c1c2439e2e356c722b","sha256:bff83a5e5802d1f5b8740acf516d76c4c20eca0ef1c692ae0a49e5266af2061b"],"state_sha256":"1e0d3d442f74c739a384c9d6c1b88f139021e8ed502624482e30463d4ed05e7d"}