{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:JDID2JEVAQ5ZZTD73FNTIICKGZ","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":"2f1731cf371608ae89d20cad77947f4501176da34277b8d0d235bdadeee23800","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-10-21T14:46:13Z","title_canon_sha256":"76f4148bb3227e35f79e2bc7f89cc0a879d1b95a0b8b67b19e3240ba1d03c057"},"schema_version":"1.0","source":{"id":"math/0510450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510450","created_at":"2026-05-18T03:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510450v1","created_at":"2026-05-18T03:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510450","created_at":"2026-05-18T03:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"JDID2JEVAQ5Z","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"JDID2JEVAQ5ZZTD7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"JDID2JEV","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e6e10ff5b56b2ea2ce7825b7c269f89ffd7e011589b3dda3eb46253d8d3d818c","target":"graph","created_at":"2026-05-18T03:39:03Z","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":"There are many theorems in the differential geometry literature of the following sort.\n  Let M be a complete Riemannian manifold with some conditions on various curvatures, diameters, volumes, etc. Then M is homotopy equivalent to a finite CW complex, or M is the interior of a compact, topological manifold with boundary.\n  At first glance it seems unlikely that such theorems have anything to say about smooth manifolds homeomorphic to R^4. However, there is a common theme to all the proofs which forbids the existence of such metrics on most (and possibly all) exotic R^4's.","authors_text":"Laurence R. Taylor","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-10-21T14:46:13Z","title":"Impossible metric conditions on exotic R^4's"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510450","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:a5fccca538f569b4ffb512e2e3b9e4206410af4490247fcc698743dc0260468e","target":"record","created_at":"2026-05-18T03:39:03Z","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":"2f1731cf371608ae89d20cad77947f4501176da34277b8d0d235bdadeee23800","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-10-21T14:46:13Z","title_canon_sha256":"76f4148bb3227e35f79e2bc7f89cc0a879d1b95a0b8b67b19e3240ba1d03c057"},"schema_version":"1.0","source":{"id":"math/0510450","kind":"arxiv","version":1}},"canonical_sha256":"48d03d2495043b9ccc7fd95b34204a367b8930e03af813b877157c9ab2de77c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48d03d2495043b9ccc7fd95b34204a367b8930e03af813b877157c9ab2de77c1","first_computed_at":"2026-05-18T03:39:03.915295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:03.915295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TAZZD3Lf9x9K+0xydDgKyVvjmVzjYL5P+wjYxbXM8DlgcvOocutPwLER8oW6oXHqhtKMuHwhxMT0tLwHZmkgDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:03.915724Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5fccca538f569b4ffb512e2e3b9e4206410af4490247fcc698743dc0260468e","sha256:e6e10ff5b56b2ea2ce7825b7c269f89ffd7e011589b3dda3eb46253d8d3d818c"],"state_sha256":"f9ec6314d18d3d6c802712ccb08395b400c70647d8db23b673a3e51fe2ca1bac"}