{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VOY5HUZRAZMF7BDY2LLKO2AZHK","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":"c20b1f7bf98d2a1214c3857fbd4be60ef0591d37ca01b28a09572a6355693646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-18T10:53:53Z","title_canon_sha256":"00f5bf222994aa2ea820672b97161f83234e8da7afa0bfd7621fef7c3b02de54"},"schema_version":"1.0","source":{"id":"1607.05011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05011","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05011v1","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05011","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"VOY5HUZRAZMF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VOY5HUZRAZMF7BDY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VOY5HUZR","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ba78d37d0280c1dc88cc061a9ce17adcdae20dee4c512301689bdb7a1c5bfe39","target":"graph","created_at":"2026-05-18T01:10:56Z","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":"We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\\widetilde M$ belonging to a certain class, then the diameter of $M$ does not exceed that of $\\widetilde M.$ Moreover, we prove that if the diameter of $M$ equals that of $\\widetilde M,$ then $M$ is isometric to the $n$-model of $\\widetilde M.$ The class of a two-sphere of revolution employed in our main theorem is very wide. For example, this class contains both ellipsoids of pro","authors_text":"Nathaphon Boonnam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-18T10:53:53Z","title":"A generalized maximal diameter sphere theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05011","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":"sha256:92447c2b2e8cb466b9e72471c94a16b95609e79f3c447ce5d990130cdd1d2288","target":"record","created_at":"2026-05-18T01:10:56Z","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":"c20b1f7bf98d2a1214c3857fbd4be60ef0591d37ca01b28a09572a6355693646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-18T10:53:53Z","title_canon_sha256":"00f5bf222994aa2ea820672b97161f83234e8da7afa0bfd7621fef7c3b02de54"},"schema_version":"1.0","source":{"id":"1607.05011","kind":"arxiv","version":1}},"canonical_sha256":"abb1d3d33106585f8478d2d6a768193a81680993396493812296f29752c45fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abb1d3d33106585f8478d2d6a768193a81680993396493812296f29752c45fbc","first_computed_at":"2026-05-18T01:10:56.132787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:56.132787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lL/ulqSqGFXfZt7Y4zAboZiBym71uSoPR1smCY9t1ehb0V7VsmPS81e6mn/YPJJcuY4DJknWAOnqJQdweMdTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:56.133280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92447c2b2e8cb466b9e72471c94a16b95609e79f3c447ce5d990130cdd1d2288","sha256:ba78d37d0280c1dc88cc061a9ce17adcdae20dee4c512301689bdb7a1c5bfe39"],"state_sha256":"1114396fee20c6d50860ec1f3aba56ae8ca84681a45ae89ea46bd8d5cc5ade3d"}