{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EULRHF6EG6RL6IOGUV7IWUAN3Z","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":"3490de49bcdf2cd86014a7b695c97a06186f924b20b12503451303b25361d5f3","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2006-10-13T21:23:12Z","title_canon_sha256":"4c96071a4af6a03d0a88bb27a422e2c7fb716d1fb3ca9747f8c489e1b9128dda"},"schema_version":"1.0","source":{"id":"math/0610439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610439","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610439v1","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610439","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"EULRHF6EG6RL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EULRHF6EG6RL6IOG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EULRHF6E","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:1f17e311ffb6a4e8d170530694302f14ba4a10cbc6a155efa4316158318cbbb7","target":"graph","created_at":"2026-05-18T04:41:06Z","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":"For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K*,V]. If K is large, its free completion under colimits is the V-category PK of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on PK.","authors_text":"Brian J. Day, Stephen Lack","cross_cats":[],"headline":"","license":"","primary_cat":"math.CT","submitted_at":"2006-10-13T21:23:12Z","title":"Limits of small functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610439","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:a246779260c9b43909f67013c663c12b6da80505a8e40af8599d5a4887717873","target":"record","created_at":"2026-05-18T04:41:06Z","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":"3490de49bcdf2cd86014a7b695c97a06186f924b20b12503451303b25361d5f3","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2006-10-13T21:23:12Z","title_canon_sha256":"4c96071a4af6a03d0a88bb27a422e2c7fb716d1fb3ca9747f8c489e1b9128dda"},"schema_version":"1.0","source":{"id":"math/0610439","kind":"arxiv","version":1}},"canonical_sha256":"25171397c437a2bf21c6a57e8b500dde7980fe7266359f08af3d35c7c0dcd300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25171397c437a2bf21c6a57e8b500dde7980fe7266359f08af3d35c7c0dcd300","first_computed_at":"2026-05-18T04:41:06.139927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:06.139927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQ42RVvhf/Q4LrZDwWrndf/OcOQHRTannQQtqhPc/u1R3JTPkPCXQ4Ml3sc1NZA/+L6XH+H9+jJzKkmwxwFgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:06.140388Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0610439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a246779260c9b43909f67013c663c12b6da80505a8e40af8599d5a4887717873","sha256:1f17e311ffb6a4e8d170530694302f14ba4a10cbc6a155efa4316158318cbbb7"],"state_sha256":"0edaa42d171f00a5163f49dd17a448daacef2ce4ac585871122c7e17bd666b39"}