{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SWU5FAXNAACKJRUNNES5XC33J7","short_pith_number":"pith:SWU5FAXN","canonical_record":{"source":{"id":"1107.0778","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-07-05T04:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"c9593de1dd59ef37f3abf2a7ac09b4e5538c6d0381ace7b6c4ad341e171bc0b9","abstract_canon_sha256":"22cdf37610f3721bacab7300a4fd62f3376c67709b3cae1603da876f3ee954dd"},"schema_version":"1.0"},"canonical_sha256":"95a9d282ed0004a4c68d6925db8b7b4fdfb0b0a3bb1351095424e7b3cdd6a4c6","source":{"kind":"arxiv","id":"1107.0778","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0778","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0778v2","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0778","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"pith_short_12","alias_value":"SWU5FAXNAACK","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SWU5FAXNAACKJRUN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SWU5FAXN","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SWU5FAXNAACKJRUNNES5XC33J7","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0778","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-07-05T04:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"c9593de1dd59ef37f3abf2a7ac09b4e5538c6d0381ace7b6c4ad341e171bc0b9","abstract_canon_sha256":"22cdf37610f3721bacab7300a4fd62f3376c67709b3cae1603da876f3ee954dd"},"schema_version":"1.0"},"canonical_sha256":"95a9d282ed0004a4c68d6925db8b7b4fdfb0b0a3bb1351095424e7b3cdd6a4c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:11.873757Z","signature_b64":"wrD4cpwQ4nNvuWRQv0Dolis1+KO4YSzvK5FoXT6LH94fm2TZCBQ2pJISzFQsw/lK7pKBp5niizSOblj+9qS8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95a9d282ed0004a4c68d6925db8b7b4fdfb0b0a3bb1351095424e7b3cdd6a4c6","last_reissued_at":"2026-05-18T04:02:11.873217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:11.873217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0778","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9W/DsytdSI1BA+c7Xk6hkHzzSdMehLwV+lFg84qIx5dJQaUJqH1deNgo0AE9H69Ah8bVuC3DLfbgR5gF7YLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:32:59.491138Z"},"content_sha256":"ae3f39bf16e53b4b80335b2b03786f255fc71f0c57b6e43e7a4a66287d9ecd58","schema_version":"1.0","event_id":"sha256:ae3f39bf16e53b4b80335b2b03786f255fc71f0c57b6e43e7a4a66287d9ecd58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SWU5FAXNAACKJRUNNES5XC33J7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lex colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Richard Garner, Stephen Lack","submitted_at":"2011-07-05T04:42:05Z","abstract_excerpt":"Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of \"exactness\" conditions between the finite limits and the specified colimits. Some examples are the notions of regular, or Barr-exact, or lextensive, or coherent, or adhesive category. We introduce a general notion of exactness, of which each of the structures listed above, and others besides, are particular instances. The notion can be understood as a form of cocompleteness \"in the lex world\" -- more precisely, in the 2-category of finitely complete categories and finite-limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0778","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xsn26v9/FVEKwTyXTkZmRlnVda++EzHgtz4GrwqzU+zvzxGYXGNSzyVNpb9ZmWzK8ozWXrqXSZLrorKlM3YhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:32:59.491502Z"},"content_sha256":"c936c439e8ad807430f227c2b1a4354e3bafb99c8ebfbbee74791072e9125c85","schema_version":"1.0","event_id":"sha256:c936c439e8ad807430f227c2b1a4354e3bafb99c8ebfbbee74791072e9125c85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWU5FAXNAACKJRUNNES5XC33J7/bundle.json","state_url":"https://pith.science/pith/SWU5FAXNAACKJRUNNES5XC33J7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWU5FAXNAACKJRUNNES5XC33J7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T15:32:59Z","links":{"resolver":"https://pith.science/pith/SWU5FAXNAACKJRUNNES5XC33J7","bundle":"https://pith.science/pith/SWU5FAXNAACKJRUNNES5XC33J7/bundle.json","state":"https://pith.science/pith/SWU5FAXNAACKJRUNNES5XC33J7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWU5FAXNAACKJRUNNES5XC33J7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SWU5FAXNAACKJRUNNES5XC33J7","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":"22cdf37610f3721bacab7300a4fd62f3376c67709b3cae1603da876f3ee954dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-07-05T04:42:05Z","title_canon_sha256":"c9593de1dd59ef37f3abf2a7ac09b4e5538c6d0381ace7b6c4ad341e171bc0b9"},"schema_version":"1.0","source":{"id":"1107.0778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0778","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0778v2","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0778","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"pith_short_12","alias_value":"SWU5FAXNAACK","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SWU5FAXNAACKJRUN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SWU5FAXN","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:c936c439e8ad807430f227c2b1a4354e3bafb99c8ebfbbee74791072e9125c85","target":"graph","created_at":"2026-05-18T04:02:11Z","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":"Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of \"exactness\" conditions between the finite limits and the specified colimits. Some examples are the notions of regular, or Barr-exact, or lextensive, or coherent, or adhesive category. We introduce a general notion of exactness, of which each of the structures listed above, and others besides, are particular instances. The notion can be understood as a form of cocompleteness \"in the lex world\" -- more precisely, in the 2-category of finitely complete categories and finite-limit","authors_text":"Richard Garner, Stephen Lack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-07-05T04:42:05Z","title":"Lex colimits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0778","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:ae3f39bf16e53b4b80335b2b03786f255fc71f0c57b6e43e7a4a66287d9ecd58","target":"record","created_at":"2026-05-18T04:02:11Z","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":"22cdf37610f3721bacab7300a4fd62f3376c67709b3cae1603da876f3ee954dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-07-05T04:42:05Z","title_canon_sha256":"c9593de1dd59ef37f3abf2a7ac09b4e5538c6d0381ace7b6c4ad341e171bc0b9"},"schema_version":"1.0","source":{"id":"1107.0778","kind":"arxiv","version":2}},"canonical_sha256":"95a9d282ed0004a4c68d6925db8b7b4fdfb0b0a3bb1351095424e7b3cdd6a4c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95a9d282ed0004a4c68d6925db8b7b4fdfb0b0a3bb1351095424e7b3cdd6a4c6","first_computed_at":"2026-05-18T04:02:11.873217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:11.873217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrD4cpwQ4nNvuWRQv0Dolis1+KO4YSzvK5FoXT6LH94fm2TZCBQ2pJISzFQsw/lK7pKBp5niizSOblj+9qS8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:11.873757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3f39bf16e53b4b80335b2b03786f255fc71f0c57b6e43e7a4a66287d9ecd58","sha256:c936c439e8ad807430f227c2b1a4354e3bafb99c8ebfbbee74791072e9125c85"],"state_sha256":"5ddadc7ab16ad4bfbb07491c6193df203dae20417a8fa98575ea8a11d8918fa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34isjQVmftT8enV4TqXHc+Ub0UyGkYXKOE9vB0heLUqQX4sFYGCOiGPxnuCh810I8rfnji+hIyjX9ET5kRAsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:32:59.493861Z","bundle_sha256":"5cc99bdf093ac3d7acdb7ff0be6ebcc76ef681a2a11d46563feb4eea5f5e89c8"}}