{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CNW6NJOFKC3WJNLQ5JMAXRPH6I","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":"fe57be8186303883716948fd7e89265a148eeed884687b6ffabbea52143b14b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-08T18:47:30Z","title_canon_sha256":"0b9d9a832ee205be31751e4333470bacd2e2e1a6f5c0eaf0cace26a02dc95104"},"schema_version":"1.0","source":{"id":"1508.01944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01944","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01944v1","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01944","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"CNW6NJOFKC3W","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CNW6NJOFKC3WJNLQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CNW6NJOF","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:bf28c50715da64280209f8c8ba26c4d12ee459ee87c7629654c899adeebaf723","target":"graph","created_at":"2026-05-18T01:35:37Z","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":"The usual construction of a CW-approximation is functorial up to homotopy, but it is not functorial. In this note, we construct a functorial CW-approximation. Our construction takes inclusions of subspaces into inclusions of subcomplexes, and commutes with intersections of subspaces of a fixed space.","authors_text":"Philip S. Hirschhorn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-08T18:47:30Z","title":"Functorial CW-approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01944","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":"sha256:9d52e4d41295d89af2375980bef318766c7352e87f45d406b0b24305b63772f5","target":"record","created_at":"2026-05-18T01:35:37Z","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":"fe57be8186303883716948fd7e89265a148eeed884687b6ffabbea52143b14b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-08T18:47:30Z","title_canon_sha256":"0b9d9a832ee205be31751e4333470bacd2e2e1a6f5c0eaf0cace26a02dc95104"},"schema_version":"1.0","source":{"id":"1508.01944","kind":"arxiv","version":1}},"canonical_sha256":"136de6a5c550b764b570ea580bc5e7f224a258ec067f2e2c67642bfe6598988b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"136de6a5c550b764b570ea580bc5e7f224a258ec067f2e2c67642bfe6598988b","first_computed_at":"2026-05-18T01:35:37.484379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:37.484379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jWDE+Q0BawCvEtdsQhW9j24KW4F47IkDqrGfD30TJGx1fij4m+mt8MwaHo0F0yeaIVdYTtkwtryAqzkZxNL2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:37.484964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d52e4d41295d89af2375980bef318766c7352e87f45d406b0b24305b63772f5","sha256:bf28c50715da64280209f8c8ba26c4d12ee459ee87c7629654c899adeebaf723"],"state_sha256":"d76bc0af8d56c5665b9118d1ea744096b1b778bdd52b3a642821d66f10c083e5"}