{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PY73WSSRZSUONX7FZLGTONHHVO","short_pith_number":"pith:PY73WSSR","schema_version":"1.0","canonical_sha256":"7e3fbb4a51cca8e6dfe5cacd3734e7aba63466d2dc81222301382d62a9e6c995","source":{"kind":"arxiv","id":"1212.5047","version":1},"attestation_state":"computed","paper":{"title":"Around the A.D. Alexandrov's theorem on a characterization of a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Victor Alexandrov","submitted_at":"2012-12-20T14:20:38Z","abstract_excerpt":"This is a survey paper on various results relates to the following theorem first proved by A.D. Alexandrov: \\textit{Let $S$ be an analytic convex sphere-homeomorphic surface in $\\mathbb R^3$ and let $k_1(\\boldsymbol{x})\\leqslant k_2(\\boldsymbol{x})$ be its principal curvatures at the point $\\boldsymbol{x}$. If the inequalities $k_1(\\boldsymbol{x})\\leqslant k\\leqslant k_2(\\boldsymbol{x})$ hold true with some constant $k$ for all $\\boldsymbol{x}\\in S$ then $S$ is a sphere.} The imphases is on a result of Y. Martinez-Maure who first proved that the above statement is not valid for convex $C^2$-su"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.5047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-20T14:20:38Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ab09e1c160d47e4fd0ed5d2b05e54513cb094593f0c27e0596b570d1e8a4ce97","abstract_canon_sha256":"13600797de123a4bea22b2e7fd22d58c00528bfac691fe21e9ef7c44f3690f1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:04.039056Z","signature_b64":"SbInFZxPupm8eowPpmZIwl7WNidguvJQDD/Ccp86V2PpcEnaRvYTH3Ib+TOQjV5KU7BRF0LeJTRVW8SDZUujCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e3fbb4a51cca8e6dfe5cacd3734e7aba63466d2dc81222301382d62a9e6c995","last_reissued_at":"2026-05-18T03:38:04.038242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:04.038242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Around the A.D. Alexandrov's theorem on a characterization of a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Victor Alexandrov","submitted_at":"2012-12-20T14:20:38Z","abstract_excerpt":"This is a survey paper on various results relates to the following theorem first proved by A.D. Alexandrov: \\textit{Let $S$ be an analytic convex sphere-homeomorphic surface in $\\mathbb R^3$ and let $k_1(\\boldsymbol{x})\\leqslant k_2(\\boldsymbol{x})$ be its principal curvatures at the point $\\boldsymbol{x}$. If the inequalities $k_1(\\boldsymbol{x})\\leqslant k\\leqslant k_2(\\boldsymbol{x})$ hold true with some constant $k$ for all $\\boldsymbol{x}\\in S$ then $S$ is a sphere.} The imphases is on a result of Y. Martinez-Maure who first proved that the above statement is not valid for convex $C^2$-su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5047","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.5047","created_at":"2026-05-18T03:38:04.038389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5047v1","created_at":"2026-05-18T03:38:04.038389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5047","created_at":"2026-05-18T03:38:04.038389+00:00"},{"alias_kind":"pith_short_12","alias_value":"PY73WSSRZSUO","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PY73WSSRZSUONX7F","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PY73WSSR","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO","json":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO.json","graph_json":"https://pith.science/api/pith-number/PY73WSSRZSUONX7FZLGTONHHVO/graph.json","events_json":"https://pith.science/api/pith-number/PY73WSSRZSUONX7FZLGTONHHVO/events.json","paper":"https://pith.science/paper/PY73WSSR"},"agent_actions":{"view_html":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO","download_json":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO.json","view_paper":"https://pith.science/paper/PY73WSSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5047&json=true","fetch_graph":"https://pith.science/api/pith-number/PY73WSSRZSUONX7FZLGTONHHVO/graph.json","fetch_events":"https://pith.science/api/pith-number/PY73WSSRZSUONX7FZLGTONHHVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO/action/storage_attestation","attest_author":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO/action/author_attestation","sign_citation":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO/action/citation_signature","submit_replication":"https://pith.science/pith/PY73WSSRZSUONX7FZLGTONHHVO/action/replication_record"}},"created_at":"2026-05-18T03:38:04.038389+00:00","updated_at":"2026-05-18T03:38:04.038389+00:00"}