{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:4C5FBB3XTTEUP4RKGG26F7NSQL","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":"d633dfedd4beb26a372fab782a3117ea0eef7063fbf3b965f85a608fb261be7e","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AT","submitted_at":"2000-04-24T20:26:45Z","title_canon_sha256":"c08b83db2521cd7fd9c5023f964a894304343ad086ee2ce575b818dee77a781a"},"schema_version":"1.0","source":{"id":"math/0004147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004147","created_at":"2026-07-04T14:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004147v1","created_at":"2026-07-04T14:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004147","created_at":"2026-07-04T14:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"4C5FBB3XTTEU","created_at":"2026-07-04T14:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"4C5FBB3XTTEUP4RK","created_at":"2026-07-04T14:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"4C5FBB3X","created_at":"2026-07-04T14:34:28Z"}],"graph_snapshots":[{"event_id":"sha256:7d978445931c3b628855cb84434f1a51d86f52901e1afaa9e3b0ed5156658f5e","target":"graph","created_at":"2026-07-04T14:34:28Z","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/0004147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the total spaces of bundles over the four sphere with fiber a three sphere up to orientation preserving and reversing homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both topologists and geometers. It has recently been shown by Grove and Ziller that each of these total spaces admits metrics with nonnegative sectional curvature.","authors_text":"Christine M. Escher, Diarmuid Crowley","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2000-04-24T20:26:45Z","title":"A classification of $S^3$-bundles over $S^4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004147","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:fa8d9e2c5c0db61e2dad6807c0e491eaf84d67fe8b4e27e401526f719b617d9b","target":"record","created_at":"2026-07-04T14:34:28Z","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":"d633dfedd4beb26a372fab782a3117ea0eef7063fbf3b965f85a608fb261be7e","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AT","submitted_at":"2000-04-24T20:26:45Z","title_canon_sha256":"c08b83db2521cd7fd9c5023f964a894304343ad086ee2ce575b818dee77a781a"},"schema_version":"1.0","source":{"id":"math/0004147","kind":"arxiv","version":1}},"canonical_sha256":"e0ba5087779cc947f22a31b5e2fdb282e0a7c6de620ad392ea86c69c0ff5d382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0ba5087779cc947f22a31b5e2fdb282e0a7c6de620ad392ea86c69c0ff5d382","first_computed_at":"2026-07-04T14:34:28.563243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:28.563243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qnEAZ72HW2sLgm3XHVyvbz2BJOJr8bRre522i0FFlWcVKnezl/bt30EcJtIsGdZjMfupiWQsJQRD9ZbwStMDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:28.564000Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0004147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa8d9e2c5c0db61e2dad6807c0e491eaf84d67fe8b4e27e401526f719b617d9b","sha256:7d978445931c3b628855cb84434f1a51d86f52901e1afaa9e3b0ed5156658f5e"],"state_sha256":"f0096e771bce981fd75a4349fd5d8c8e55d375959b65356a646c27a5b3965808"}