{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3NYH525664CFTVTGWIJJ4ISV4P","short_pith_number":"pith:3NYH5256","canonical_record":{"source":{"id":"1103.4485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-03-23T10:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"6224c38a8bb7fca812e5ca4f19f6febf95a723ce8fec940f39f1ab21c2a992ee","abstract_canon_sha256":"c50b403da544326ec43c6c52f5daf391b4a0be65f2c29c961eb35d5d90dc4e1d"},"schema_version":"1.0"},"canonical_sha256":"db707eebbef70459d666b2129e2255e3f14c6f964540e3f4f88d17a8142228c4","source":{"kind":"arxiv","id":"1103.4485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4485","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4485v1","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4485","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"3NYH525664CF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3NYH525664CFTVTG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3NYH5256","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3NYH525664CFTVTGWIJJ4ISV4P","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-03-23T10:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"6224c38a8bb7fca812e5ca4f19f6febf95a723ce8fec940f39f1ab21c2a992ee","abstract_canon_sha256":"c50b403da544326ec43c6c52f5daf391b4a0be65f2c29c961eb35d5d90dc4e1d"},"schema_version":"1.0"},"canonical_sha256":"db707eebbef70459d666b2129e2255e3f14c6f964540e3f4f88d17a8142228c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.939002Z","signature_b64":"tiTqyjzCPFo/Qcx06yIvFKqQAhw2hbCph7jaODot1RFuXmtIFaUxlp4JIrt3GpEDSe5dV5Bj1L4FLx6pCmVTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db707eebbef70459d666b2129e2255e3f14c6f964540e3f4f88d17a8142228c4","last_reissued_at":"2026-05-18T04:26:01.938589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.938589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4485","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":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McipLsx1NAyzOYFbq6Z4jNQkZ8ysOmDIuhj9tbAmzxYD52OGbtQpYZdgwsx7xnRhdN5nut8mCFRG5/Q0FWhACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:19:10.105747Z"},"content_sha256":"ee2c2a0f000e1605e6ab0a1ba63caeb63901cb290c50cafb0418abce829e900a","schema_version":"1.0","event_id":"sha256:ee2c2a0f000e1605e6ab0a1ba63caeb63901cb290c50cafb0418abce829e900a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3NYH525664CFTVTGWIJJ4ISV4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A homotopy colimit theorem for diagrams of braided monoidal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"A.R. Garz\\'on, R. P\\'erez","submitted_at":"2011-03-23T10:36:01Z","abstract_excerpt":"Thomason's Homotopy Colimit Theorem has been extended to bicategories and this extension can be adapted, through the delooping principle, to a corresponding theorem for diagrams of monoidal categories. In this version, we show that the homotopy type of the diagram can be also represented by a genuine simplicial set nerve associated with it. This suggests the study of a homotopy colimit theorem, for diagrams $\\b$ of braided monoidal categories, by means of a simplicial set {\\em nerve of the diagram}. We prove that it is weak homotopy equivalent to the homotopy colimit of the diagram, of simplic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4485","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":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXN7Vf9li+ZKhp26AXbk/JdLUrrbhGmohfYt2pzj085PYksicBjtDD+iA+qfrgIwMpma+LS6rUROFfD62XolCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:19:10.106090Z"},"content_sha256":"afbabe7d199bff0d275c34013e8c8436c91f442177c5cb22ecebdb28d9724170","schema_version":"1.0","event_id":"sha256:afbabe7d199bff0d275c34013e8c8436c91f442177c5cb22ecebdb28d9724170"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NYH525664CFTVTGWIJJ4ISV4P/bundle.json","state_url":"https://pith.science/pith/3NYH525664CFTVTGWIJJ4ISV4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NYH525664CFTVTGWIJJ4ISV4P/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":"2026-06-30T22:19:10Z","links":{"resolver":"https://pith.science/pith/3NYH525664CFTVTGWIJJ4ISV4P","bundle":"https://pith.science/pith/3NYH525664CFTVTGWIJJ4ISV4P/bundle.json","state":"https://pith.science/pith/3NYH525664CFTVTGWIJJ4ISV4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NYH525664CFTVTGWIJJ4ISV4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3NYH525664CFTVTGWIJJ4ISV4P","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":"c50b403da544326ec43c6c52f5daf391b4a0be65f2c29c961eb35d5d90dc4e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-03-23T10:36:01Z","title_canon_sha256":"6224c38a8bb7fca812e5ca4f19f6febf95a723ce8fec940f39f1ab21c2a992ee"},"schema_version":"1.0","source":{"id":"1103.4485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4485","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4485v1","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4485","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"3NYH525664CF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3NYH525664CFTVTG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3NYH5256","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:afbabe7d199bff0d275c34013e8c8436c91f442177c5cb22ecebdb28d9724170","target":"graph","created_at":"2026-05-18T04:26:01Z","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":"Thomason's Homotopy Colimit Theorem has been extended to bicategories and this extension can be adapted, through the delooping principle, to a corresponding theorem for diagrams of monoidal categories. In this version, we show that the homotopy type of the diagram can be also represented by a genuine simplicial set nerve associated with it. This suggests the study of a homotopy colimit theorem, for diagrams $\\b$ of braided monoidal categories, by means of a simplicial set {\\em nerve of the diagram}. We prove that it is weak homotopy equivalent to the homotopy colimit of the diagram, of simplic","authors_text":"A.R. Garz\\'on, R. P\\'erez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-03-23T10:36:01Z","title":"A homotopy colimit theorem for diagrams of braided monoidal categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4485","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:ee2c2a0f000e1605e6ab0a1ba63caeb63901cb290c50cafb0418abce829e900a","target":"record","created_at":"2026-05-18T04:26:01Z","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":"c50b403da544326ec43c6c52f5daf391b4a0be65f2c29c961eb35d5d90dc4e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-03-23T10:36:01Z","title_canon_sha256":"6224c38a8bb7fca812e5ca4f19f6febf95a723ce8fec940f39f1ab21c2a992ee"},"schema_version":"1.0","source":{"id":"1103.4485","kind":"arxiv","version":1}},"canonical_sha256":"db707eebbef70459d666b2129e2255e3f14c6f964540e3f4f88d17a8142228c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db707eebbef70459d666b2129e2255e3f14c6f964540e3f4f88d17a8142228c4","first_computed_at":"2026-05-18T04:26:01.938589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:01.938589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tiTqyjzCPFo/Qcx06yIvFKqQAhw2hbCph7jaODot1RFuXmtIFaUxlp4JIrt3GpEDSe5dV5Bj1L4FLx6pCmVTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:01.939002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee2c2a0f000e1605e6ab0a1ba63caeb63901cb290c50cafb0418abce829e900a","sha256:afbabe7d199bff0d275c34013e8c8436c91f442177c5cb22ecebdb28d9724170"],"state_sha256":"4360dd88bd4346b32ea8c1747e8715c1404d42b95266cf0cf863412838130649"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aiUu0vonIVkiwWZUaThDz+C80uZX8HKVxSp/GLKwNXFl9UGU4AB5dgn7d0yqZ3GXFwij4y9dzzTJnZozYdT8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:19:10.108074Z","bundle_sha256":"791e1cb840ba587e639671e28f38da2812e4ed43753dbb6a5ab34adc1ca7b6a4"}}