{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UASKAOZBGP427WFQUWLREVA72C","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":"84cc97c72b1566a2e411611139bdc887b38566ce8fc97cb940fc2afa46aa1e85","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-02T02:59:27Z","title_canon_sha256":"c7bf272fdf79244b9b89be0417853865c18610e0601971127c96e09f9d0c95d3"},"schema_version":"1.0","source":{"id":"1201.0415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0415","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0415v2","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0415","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"UASKAOZBGP42","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UASKAOZBGP427WFQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UASKAOZB","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f58c9f2143c39d49a5dd792ebe05f2459c3d9ebc9947c200b553ad47bf135205","target":"graph","created_at":"2026-05-18T02:03:56Z","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 smallest $r$ so that a metric $r$-ball covers a metric space $M$ is called the radius of $M$. The volume of a metric $r$-ball in the space form of constant curvature $k$ is an upper bound for the volume of any Riemannian manifold with sectional curvature $\\geq k$ and radius $\\leq r$. We show that when such a manifold has volume almost equal to this upper bound, it is diffeomorphic to a sphere or a real projective space.","authors_text":"Curtis Pro, Frederick Wilhelm, Michael Sill","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-02T02:59:27Z","title":"The Diffeomorphism Type of Manifolds with Almost Maximal Volume"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0415","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":"sha256:3ac5856667e50892079e50913a434ca42c245a6d604904195a92477d892af273","target":"record","created_at":"2026-05-18T02:03:56Z","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":"84cc97c72b1566a2e411611139bdc887b38566ce8fc97cb940fc2afa46aa1e85","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-02T02:59:27Z","title_canon_sha256":"c7bf272fdf79244b9b89be0417853865c18610e0601971127c96e09f9d0c95d3"},"schema_version":"1.0","source":{"id":"1201.0415","kind":"arxiv","version":2}},"canonical_sha256":"a024a03b2133f9afd8b0a59712541fd092dfa7514b0cf906658ffd6a9362dea4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a024a03b2133f9afd8b0a59712541fd092dfa7514b0cf906658ffd6a9362dea4","first_computed_at":"2026-05-18T02:03:56.006565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:56.006565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NpMPzAT/O4gyYtu2g/kNrT2jGCDfRQfU2NiOKBldjXNXKguPXmq/EoRb+ZCVkJs7tmbHCffv1OrlnQhT4LjmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:56.007279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ac5856667e50892079e50913a434ca42c245a6d604904195a92477d892af273","sha256:f58c9f2143c39d49a5dd792ebe05f2459c3d9ebc9947c200b553ad47bf135205"],"state_sha256":"e50825008f07b7a6f172e7e8a66b63b4b0345e7c783a1f17f19233f7f09ac1e6"}