{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6LFLFHFKZHKTZZ62BISBKTP67L","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":"418aca41e02b52204ef3856ef7c6390e9f7d5479230e5de317d86c29330cebe7","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-01-24T17:14:14Z","title_canon_sha256":"03e9bd8251d51549004fab8d909133420cfe4dc367e9832abff788166a759e34"},"schema_version":"1.0","source":{"id":"1101.4594","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4594","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4594v2","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4594","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"pith_short_12","alias_value":"6LFLFHFKZHKT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LFLFHFKZHKTZZ62","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LFLFHFK","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:d1c6298fc67b973b464df4c3dcdaf70d543d2345f6d636d26170e155fa44c473","target":"graph","created_at":"2026-05-18T01:37:39Z","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":"Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicategory of spans, provided that the category has pullbacks and enough colimits.","authors_text":"ECS, France), Pawel Sobocinski (DSSE, Tobias Heindel (Laboratoire d'Informatique de Paris-Nord, Universit\\'e de Paris, University of Southampton)","cross_cats":["cs.PL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-01-24T17:14:14Z","title":"Being Van Kampen is a universal property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4594","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":"sha256:7d75388929e9dbf472af69e23a51f72123699adad67ecbd21cac6af5a50408b1","target":"record","created_at":"2026-05-18T01:37:39Z","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":"418aca41e02b52204ef3856ef7c6390e9f7d5479230e5de317d86c29330cebe7","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-01-24T17:14:14Z","title_canon_sha256":"03e9bd8251d51549004fab8d909133420cfe4dc367e9832abff788166a759e34"},"schema_version":"1.0","source":{"id":"1101.4594","kind":"arxiv","version":2}},"canonical_sha256":"f2cab29caac9d53ce7da0a24154dfefae0b4734aabacb76483d210735018fac1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2cab29caac9d53ce7da0a24154dfefae0b4734aabacb76483d210735018fac1","first_computed_at":"2026-05-18T01:37:39.674454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:39.674454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQJP09Nb8B1EPZVnuhO0DGMFlfU8Qit3CdL4d70FMD9gA8f0+ii8+QjaZb6TuuJGhmw5BOw/DJJWb+YU7TN0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:39.675070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4594","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d75388929e9dbf472af69e23a51f72123699adad67ecbd21cac6af5a50408b1","sha256:d1c6298fc67b973b464df4c3dcdaf70d543d2345f6d636d26170e155fa44c473"],"state_sha256":"1cdb1964a3f544d7dd9b0180b2d6d0df04f1e537cd08e1956d44357f894e5ba5"}