{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:M7CKFVNYO7P4Q4GXJ4GC6JSM7N","short_pith_number":"pith:M7CKFVNY","schema_version":"1.0","canonical_sha256":"67c4a2d5b877dfc870d74f0c2f264cfb737e1c76506ac88ac4d1be642d544e6a","source":{"kind":"arxiv","id":"2506.08246","version":1},"attestation_state":"computed","paper":{"title":"Thomason's colimit theorem for the double category of elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Andrew Gill, Maru Sarazola","submitted_at":"2025-06-09T21:26:12Z","abstract_excerpt":"We show that, for any 2-category $C$ and 2-functor $F\\colon C \\to Cat$, the double category of elements $\\iint_C F$ introduced by Grandis and Par\\'e satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy equivalence $B hocolim F\\simeq B(\\iint_C F)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.08246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-06-09T21:26:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8a2c99bc53311dd45b09b2bb5096a6bbd9d34581de24fcfb6a94234a05912a15","abstract_canon_sha256":"6e5303de18a748ed92cbcc3c1b73e54df5d176cd096c9c14866c39eee7981c87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:46.835711Z","signature_b64":"km5bnVKfWsVFXJTqOEve5vJgusXJXxem+NNDIM6XsnM7wgMBP5FcT2mXc92NL/h3lJ24GMrlQbjIdTIHBApoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c4a2d5b877dfc870d74f0c2f264cfb737e1c76506ac88ac4d1be642d544e6a","last_reissued_at":"2026-07-05T11:18:46.835083Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:46.835083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thomason's colimit theorem for the double category of elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Andrew Gill, Maru Sarazola","submitted_at":"2025-06-09T21:26:12Z","abstract_excerpt":"We show that, for any 2-category $C$ and 2-functor $F\\colon C \\to Cat$, the double category of elements $\\iint_C F$ introduced by Grandis and Par\\'e satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy equivalence $B hocolim F\\simeq B(\\iint_C F)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08246","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08246/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.08246","created_at":"2026-07-05T11:18:46.835146+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08246v1","created_at":"2026-07-05T11:18:46.835146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08246","created_at":"2026-07-05T11:18:46.835146+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7CKFVNYO7P4","created_at":"2026-07-05T11:18:46.835146+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7CKFVNYO7P4Q4GX","created_at":"2026-07-05T11:18:46.835146+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7CKFVNY","created_at":"2026-07-05T11:18:46.835146+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N","json":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N.json","graph_json":"https://pith.science/api/pith-number/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/graph.json","events_json":"https://pith.science/api/pith-number/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/events.json","paper":"https://pith.science/paper/M7CKFVNY"},"agent_actions":{"view_html":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N","download_json":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N.json","view_paper":"https://pith.science/paper/M7CKFVNY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08246&json=true","fetch_graph":"https://pith.science/api/pith-number/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/graph.json","fetch_events":"https://pith.science/api/pith-number/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/action/storage_attestation","attest_author":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/action/author_attestation","sign_citation":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/action/citation_signature","submit_replication":"https://pith.science/pith/M7CKFVNYO7P4Q4GXJ4GC6JSM7N/action/replication_record"}},"created_at":"2026-07-05T11:18:46.835146+00:00","updated_at":"2026-07-05T11:18:46.835146+00:00"}