{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5C6JLWGVPFF4XEOXTQN7FMEOYZ","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":"59f93ea596fa32de9f9a143a470e4d043c814c100a21b16596a4d9569f728d5b","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-23T15:51:43Z","title_canon_sha256":"bb7698ccfc7e0fe9588a2c8663158bc07ff31b4750df47667862918ba995b144"},"schema_version":"1.0","source":{"id":"1202.5215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5215","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5215v1","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5215","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"5C6JLWGVPFF4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5C6JLWGVPFF4XEOX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5C6JLWGV","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:56de616afee2a160bc1d8ff9f32f129251f30054d7ba68dc5b0576b5fece047a","target":"graph","created_at":"2026-05-18T02:41:26Z","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 give a sharper version of a theorem of Rosicky, Trnkova and Adamek, and a new proof of a theorem of Rosicky, both about colimit preservation between categories of structures. Unlike the original proofs, which use category-theoretic methods, we use set-theoretic arguments involving elementary embeddings given by large cardinals such as alpha-strongly compact and C^(n)-extendible cardinals.","authors_text":"Andrew Brooke-Taylor, Joan Bagaria","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-23T15:51:43Z","title":"On colimits and elementary embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5215","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":"sha256:0b60095108d5db623ef05cece3a2af499cedd8c648e7bf7219b6175fa2866cb5","target":"record","created_at":"2026-05-18T02:41:26Z","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":"59f93ea596fa32de9f9a143a470e4d043c814c100a21b16596a4d9569f728d5b","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-23T15:51:43Z","title_canon_sha256":"bb7698ccfc7e0fe9588a2c8663158bc07ff31b4750df47667862918ba995b144"},"schema_version":"1.0","source":{"id":"1202.5215","kind":"arxiv","version":1}},"canonical_sha256":"e8bc95d8d5794bcb91d79c1bf2b08ec66cdbf9c9e42fd2f6ab77b47a1ddc7d08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8bc95d8d5794bcb91d79c1bf2b08ec66cdbf9c9e42fd2f6ab77b47a1ddc7d08","first_computed_at":"2026-05-18T02:41:26.415393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.415393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ae5tuW/3MVUVAoj574z76OQaCIWxBlehp3BNX49YSY2rwi+VJd3HK5lKXSJasFa/cqOlyOIJSL9OIGNTDw73Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.415804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b60095108d5db623ef05cece3a2af499cedd8c648e7bf7219b6175fa2866cb5","sha256:56de616afee2a160bc1d8ff9f32f129251f30054d7ba68dc5b0576b5fece047a"],"state_sha256":"03341dc00bc4b0bfb1efb1fd8d94a978607f303df56a550589ae86d66f1be766"}