{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:4LHUS4ICTRKOGMZWHZK7PXZYO7","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":"dd5d58f1a002c202d19aa18c32f2e12d6cb52ca89d4bcff8d2ca10f95269c0b9","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2001-11-27T20:52:24Z","title_canon_sha256":"6c01081c6cfcbb73086ef8eae38e1807b702ddf25a4c48f3b280a20bb2953220"},"schema_version":"1.0","source":{"id":"math/0111287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0111287","created_at":"2026-07-04T14:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/0111287v1","created_at":"2026-07-04T14:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0111287","created_at":"2026-07-04T14:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"4LHUS4ICTRKO","created_at":"2026-07-04T14:35:46Z"},{"alias_kind":"pith_short_16","alias_value":"4LHUS4ICTRKOGMZW","created_at":"2026-07-04T14:35:46Z"},{"alias_kind":"pith_short_8","alias_value":"4LHUS4IC","created_at":"2026-07-04T14:35:46Z"}],"graph_snapshots":[{"event_id":"sha256:1fcc7c69385555fa869d16ccbe8cbd93a2df78ec3756352fb82147d53602fccb","target":"graph","created_at":"2026-07-04T14:35:46Z","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/0111287/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields.","authors_text":"Daniel C. Isaksen, Daniel Dugger","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2001-11-27T20:52:24Z","title":"Hypercovers in topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111287","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":"sha256:398ab516e7a231369fd99b70ef78cff9a0e8c1cb9ea300346e4f794fdaa655d0","target":"record","created_at":"2026-07-04T14:35:46Z","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":"dd5d58f1a002c202d19aa18c32f2e12d6cb52ca89d4bcff8d2ca10f95269c0b9","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2001-11-27T20:52:24Z","title_canon_sha256":"6c01081c6cfcbb73086ef8eae38e1807b702ddf25a4c48f3b280a20bb2953220"},"schema_version":"1.0","source":{"id":"math/0111287","kind":"arxiv","version":1}},"canonical_sha256":"e2cf4971029c54e333363e55f7df3877cf29164bf6ce6da6ae8c42c556b7c64b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2cf4971029c54e333363e55f7df3877cf29164bf6ce6da6ae8c42c556b7c64b","first_computed_at":"2026-07-04T14:35:46.664196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:46.664196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbScv+yNLCrPeKggcwxN+uklAYjLlcDAaNYBdVq+Vt6SYaZtMkgVvMlcNiscxn0FfQl7azJaS3IGpvEbIcO9Bw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:46.664598Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0111287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:398ab516e7a231369fd99b70ef78cff9a0e8c1cb9ea300346e4f794fdaa655d0","sha256:1fcc7c69385555fa869d16ccbe8cbd93a2df78ec3756352fb82147d53602fccb"],"state_sha256":"7debf473da245486848e164fdac875ac7bb3e401d73006e28c7e5ecdc3781c5b"}