{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:Q77AALYZ472ZAAGHVGJOYWWFAY","short_pith_number":"pith:Q77AALYZ","canonical_record":{"source":{"id":"0903.5058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-03-30T15:40:03Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a0a9dd25e057debbccbeebbb9212feb4c4d4e31d26cd9a77c78507e11423dca1","abstract_canon_sha256":"393206e83ad5420a33d666a231a71d24a46f72e46c2e90673eca0588bd6d8047"},"schema_version":"1.0"},"canonical_sha256":"87fe002f19e7f59000c7a992ec5ac50639fa6ee480388b14ccbf46277084d85d","source":{"kind":"arxiv","id":"0903.5058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.5058","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0903.5058v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.5058","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"Q77AALYZ472Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"Q77AALYZ472ZAAGH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"Q77AALYZ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:Q77AALYZ472ZAAGHVGJOYWWFAY","target":"record","payload":{"canonical_record":{"source":{"id":"0903.5058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-03-30T15:40:03Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a0a9dd25e057debbccbeebbb9212feb4c4d4e31d26cd9a77c78507e11423dca1","abstract_canon_sha256":"393206e83ad5420a33d666a231a71d24a46f72e46c2e90673eca0588bd6d8047"},"schema_version":"1.0"},"canonical_sha256":"87fe002f19e7f59000c7a992ec5ac50639fa6ee480388b14ccbf46277084d85d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.304978Z","signature_b64":"gSw9+1hz+8SLjJ2joBGYsH8s6nyD00FiHNo/E+75v9ZdQTSRz7n26+MS3yTu5Yd8J5+FBaytdrZ6HZQpcQAwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87fe002f19e7f59000c7a992ec5ac50639fa6ee480388b14ccbf46277084d85d","last_reissued_at":"2026-05-18T02:41:51.304436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.304436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.5058","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLKUIjrq3tUWkLxCIM8lpGmSTe2NOO6LmGIT6lwaONS0rRvI6mJrMVieCxUYcql2ySD+gOGfx+BuxczVZ6+fAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:59:00.738452Z"},"content_sha256":"63b78c4c8fde10e4435b2cc6a7f75fce40aea47b12cfda2d4de1223eb8db3ac9","schema_version":"1.0","event_id":"sha256:63b78c4c8fde10e4435b2cc6a7f75fce40aea47b12cfda2d4de1223eb8db3ac9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:Q77AALYZ472ZAAGHVGJOYWWFAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nerves and classifying spaces for bicategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"A.M. Cegarra, A.R. Garz\\'on, P. Carrasco","submitted_at":"2009-03-30T15:40:03Z","abstract_excerpt":"This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate `nerves of C' are homotopy equivalent. Any one of these realizations could therefore be taken as the classifying space BC of the bicategory. Its other major result proves a direct extension of Thomason's `Homotopy Colimit Theorem' to bicategories: When the homotopy colimit construction is carried out on a diagram of spaces obtained by applying the classifying spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5058","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":""},"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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FEs1AVQNfjyZDeOV0q/Aqdcmfo257NzqhMUTSXx6vp3Bvy4DDzT04vmqE3DU174R717OAEObSiQISxtAtVxvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:59:00.738959Z"},"content_sha256":"f6b06394420f7e4c3a6af2920ac04564ac7c83ff13a4ad11c7df37be69be2f23","schema_version":"1.0","event_id":"sha256:f6b06394420f7e4c3a6af2920ac04564ac7c83ff13a4ad11c7df37be69be2f23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/bundle.json","state_url":"https://pith.science/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/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":"2026-06-30T03:59:00Z","links":{"resolver":"https://pith.science/pith/Q77AALYZ472ZAAGHVGJOYWWFAY","bundle":"https://pith.science/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/bundle.json","state":"https://pith.science/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q77AALYZ472ZAAGHVGJOYWWFAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Q77AALYZ472ZAAGHVGJOYWWFAY","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":"393206e83ad5420a33d666a231a71d24a46f72e46c2e90673eca0588bd6d8047","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-03-30T15:40:03Z","title_canon_sha256":"a0a9dd25e057debbccbeebbb9212feb4c4d4e31d26cd9a77c78507e11423dca1"},"schema_version":"1.0","source":{"id":"0903.5058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.5058","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0903.5058v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.5058","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"Q77AALYZ472Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"Q77AALYZ472ZAAGH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"Q77AALYZ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:f6b06394420f7e4c3a6af2920ac04564ac7c83ff13a4ad11c7df37be69be2f23","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate `nerves of C' are homotopy equivalent. Any one of these realizations could therefore be taken as the classifying space BC of the bicategory. Its other major result proves a direct extension of Thomason's `Homotopy Colimit Theorem' to bicategories: When the homotopy colimit construction is carried out on a diagram of spaces obtained by applying the classifying spa","authors_text":"A.M. Cegarra, A.R. Garz\\'on, P. Carrasco","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-03-30T15:40:03Z","title":"Nerves and classifying spaces for bicategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5058","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":"sha256:63b78c4c8fde10e4435b2cc6a7f75fce40aea47b12cfda2d4de1223eb8db3ac9","target":"record","created_at":"2026-05-18T02:41:51Z","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":"393206e83ad5420a33d666a231a71d24a46f72e46c2e90673eca0588bd6d8047","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-03-30T15:40:03Z","title_canon_sha256":"a0a9dd25e057debbccbeebbb9212feb4c4d4e31d26cd9a77c78507e11423dca1"},"schema_version":"1.0","source":{"id":"0903.5058","kind":"arxiv","version":1}},"canonical_sha256":"87fe002f19e7f59000c7a992ec5ac50639fa6ee480388b14ccbf46277084d85d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87fe002f19e7f59000c7a992ec5ac50639fa6ee480388b14ccbf46277084d85d","first_computed_at":"2026-05-18T02:41:51.304436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.304436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSw9+1hz+8SLjJ2joBGYsH8s6nyD00FiHNo/E+75v9ZdQTSRz7n26+MS3yTu5Yd8J5+FBaytdrZ6HZQpcQAwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.304978Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.5058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b78c4c8fde10e4435b2cc6a7f75fce40aea47b12cfda2d4de1223eb8db3ac9","sha256:f6b06394420f7e4c3a6af2920ac04564ac7c83ff13a4ad11c7df37be69be2f23"],"state_sha256":"53116c45a47137cc0d157325d1e7a420f0d96f32a2c5e0bb2ca95c6b26286ca4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/Tr3sXZpeuDGZxqeA6ynonkL71EAQOVz6x+DlMI4qbXDOXbOv/BzqVtb85EwPfbClq7glQBpLLq+kF+jI/QAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:59:00.741339Z","bundle_sha256":"b7250a1ec3b377abe983adab9af57de6a9eb5d24c7b78aa533cfc2c61cb5baf0"}}