{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:LXRE5Y43HJKN73K7VFCTECD67S","short_pith_number":"pith:LXRE5Y43","canonical_record":{"source":{"id":"math/9811038","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"1998-11-06T21:36:07Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"65fbcaeaae02fb02c684b594b64f41612af726344e44202ee4cf3d9720ba7644","abstract_canon_sha256":"ddabcfd226434c468ad71cbe07c11ffbe6652ea6bb21faa2cf31068045ae8735"},"schema_version":"1.0"},"canonical_sha256":"5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4","source":{"kind":"arxiv","id":"math/9811038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9811038","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9811038v2","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9811038","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"LXRE5Y43HJKN","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXRE5Y43HJKN73K7","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXRE5Y43","created_at":"2026-07-04T14:40:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:LXRE5Y43HJKN73K7VFCTECD67S","target":"record","payload":{"canonical_record":{"source":{"id":"math/9811038","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"1998-11-06T21:36:07Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"65fbcaeaae02fb02c684b594b64f41612af726344e44202ee4cf3d9720ba7644","abstract_canon_sha256":"ddabcfd226434c468ad71cbe07c11ffbe6652ea6bb21faa2cf31068045ae8735"},"schema_version":"1.0"},"canonical_sha256":"5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:51.470729Z","signature_b64":"KfJqljoH8wozpB58cevA8Ws5MvA1X8zNw6pYkAR8ZEG5YzU2xAPMZD6QrfzfGNvZCvjqquJmGkvDUDjNRBKdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4","last_reissued_at":"2026-07-04T14:40:51.470373Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:51.470373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9811038","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KguHq85uHHZ6DfBG5cw3lx9D+I8byn7ZURO5eEVZQRJb2L7cnsYlES9U/lJEnfy5IzM1AAPLIjYXFU1e2gm5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:10:18.654044Z"},"content_sha256":"ea350a2171ce64e0d81a4782a0cc5427201dece146c5db0bcdfa9005fca658af","schema_version":"1.0","event_id":"sha256:ea350a2171ce64e0d81a4782a0cc5427201dece146c5db0bcdfa9005fca658af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:LXRE5Y43HJKN73K7VFCTECD67S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fibrations and homotopy colimits of simplicial sheaves","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Charles Rezk","submitted_at":"1998-11-06T21:36:07Z","abstract_excerpt":"We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the notion of a quasi-fibration of spaces, and seems to be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9811038","kind":"arxiv","version":2},"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/math/9811038/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABEWfQfObYBNBKD+UHUZfLkpNwkdVE0DR2h3SRLfXqqnwEiDW/OxnMkb2gAJIWnsuI6anlmBrfLO87/s8Ln1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:10:18.655070Z"},"content_sha256":"6a05cf5559912d9a1d320a397eb931246e8358491613110f9032b14d62c178c7","schema_version":"1.0","event_id":"sha256:6a05cf5559912d9a1d320a397eb931246e8358491613110f9032b14d62c178c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXRE5Y43HJKN73K7VFCTECD67S/bundle.json","state_url":"https://pith.science/pith/LXRE5Y43HJKN73K7VFCTECD67S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXRE5Y43HJKN73K7VFCTECD67S/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":"2026-08-10T19:10:18Z","links":{"resolver":"https://pith.science/pith/LXRE5Y43HJKN73K7VFCTECD67S","bundle":"https://pith.science/pith/LXRE5Y43HJKN73K7VFCTECD67S/bundle.json","state":"https://pith.science/pith/LXRE5Y43HJKN73K7VFCTECD67S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXRE5Y43HJKN73K7VFCTECD67S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:LXRE5Y43HJKN73K7VFCTECD67S","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":"ddabcfd226434c468ad71cbe07c11ffbe6652ea6bb21faa2cf31068045ae8735","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.AT","submitted_at":"1998-11-06T21:36:07Z","title_canon_sha256":"65fbcaeaae02fb02c684b594b64f41612af726344e44202ee4cf3d9720ba7644"},"schema_version":"1.0","source":{"id":"math/9811038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9811038","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9811038v2","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9811038","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"LXRE5Y43HJKN","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXRE5Y43HJKN73K7","created_at":"2026-07-04T14:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXRE5Y43","created_at":"2026-07-04T14:40:51Z"}],"graph_snapshots":[{"event_id":"sha256:6a05cf5559912d9a1d320a397eb931246e8358491613110f9032b14d62c178c7","target":"graph","created_at":"2026-07-04T14:40:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9811038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the notion of a quasi-fibration of spaces, and seems to be of independent interest.","authors_text":"Charles Rezk","cross_cats":["math.CT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"1998-11-06T21:36:07Z","title":"Fibrations and homotopy colimits of simplicial sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9811038","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:ea350a2171ce64e0d81a4782a0cc5427201dece146c5db0bcdfa9005fca658af","target":"record","created_at":"2026-07-04T14:40:51Z","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":"ddabcfd226434c468ad71cbe07c11ffbe6652ea6bb21faa2cf31068045ae8735","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.AT","submitted_at":"1998-11-06T21:36:07Z","title_canon_sha256":"65fbcaeaae02fb02c684b594b64f41612af726344e44202ee4cf3d9720ba7644"},"schema_version":"1.0","source":{"id":"math/9811038","kind":"arxiv","version":2}},"canonical_sha256":"5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4","first_computed_at":"2026-07-04T14:40:51.470373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:51.470373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KfJqljoH8wozpB58cevA8Ws5MvA1X8zNw6pYkAR8ZEG5YzU2xAPMZD6QrfzfGNvZCvjqquJmGkvDUDjNRBKdAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:51.470729Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9811038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea350a2171ce64e0d81a4782a0cc5427201dece146c5db0bcdfa9005fca658af","sha256:6a05cf5559912d9a1d320a397eb931246e8358491613110f9032b14d62c178c7"],"state_sha256":"dbd1bfb7e493e6cd9fe2d5dd86d006c36119c761f269c3217451a01341aa69d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMxvI5nn+uk4ZwXSClchcO3ZtZbYy+tko3sPrxC6jg9HRMifN7cjf0dUJGxSRJgOzRiNHUJ4c/TUuWFrZPEgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:10:18.660563Z","bundle_sha256":"24ca715be55b9c178772b038248990f9725f03dbef72d1dc4f1b67289c1ca1c4"}}