{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CIN2EP3NH276LCNPAI753BNZBM","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":"3a5c705d82073afb252e4c093e2f2e83e364ec26ec9bb746fd01c3d648dbf552","cross_cats_sorted":["math.OA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-02T12:09:43Z","title_canon_sha256":"9a2d91dcdb4d3a76335cf2c0d33607cecfceb0b8b164c55104735537f6406a11"},"schema_version":"1.0","source":{"id":"1312.0432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0432","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0432v1","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0432","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"CIN2EP3NH276","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CIN2EP3NH276LCNP","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CIN2EP3N","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:475026b48dfee5726124decf4094ac87337094fc014ad740b2b87a183061693c","target":"graph","created_at":"2026-05-18T03:05:45Z","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":"Using the general notions of finitely presentable and finitely generated object introduced by Gabriel and Ulmer in 1971, we prove that, in any (locally small) category, two sequences of finitely presentable objects and morphisms (or two sequences of finitely generated objects and monomorphisms) have isomorphic colimits (=direct limits) if, and only if, they are confluent. The latter means that the two given sequences can be connected by a back-and-forth chain of morphisms that is cofinal on each side, and commutes with the sequences at each finite stage. In several concrete situations, analogo","authors_text":"Luca Spada, Vincenzo Marra","cross_cats":["math.OA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-02T12:09:43Z","title":"Two isomorphism criteria for directed colimits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0432","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":"sha256:1f80085eade97bbd08a3ecfc7aa363ea9b8a79239488c71e1188b65c25fb1733","target":"record","created_at":"2026-05-18T03:05:45Z","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":"3a5c705d82073afb252e4c093e2f2e83e364ec26ec9bb746fd01c3d648dbf552","cross_cats_sorted":["math.OA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-02T12:09:43Z","title_canon_sha256":"9a2d91dcdb4d3a76335cf2c0d33607cecfceb0b8b164c55104735537f6406a11"},"schema_version":"1.0","source":{"id":"1312.0432","kind":"arxiv","version":1}},"canonical_sha256":"121ba23f6d3ebfe589af023fdd85b90b2091337711a1dad976abd00c33cd9e1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"121ba23f6d3ebfe589af023fdd85b90b2091337711a1dad976abd00c33cd9e1b","first_computed_at":"2026-05-18T03:05:45.706864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:45.706864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8bY1igmViLW2cFuXyMcmmrADfkteaB2pBuwFNzu+breN/lZ/senwLDY5eAJPf2FsTrVuHvMgs9q8bo+1YE11Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:45.707420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f80085eade97bbd08a3ecfc7aa363ea9b8a79239488c71e1188b65c25fb1733","sha256:475026b48dfee5726124decf4094ac87337094fc014ad740b2b87a183061693c"],"state_sha256":"4bac239e3ae42991ea6295058e3cfb28760e9b42d67eb4341c299add0e9245cf"}