{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6KDXIVFQE2ZFMSFQ577DA57CFI","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":"1f4027798ba89302a06743a8851cfbe3aaa661a080b49921a69f2031ba444eab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-01T11:38:04Z","title_canon_sha256":"1d7e4b8584580ed32f2c308338fc4b3fc35682dc36f95dd249270dd1cd99d23b"},"schema_version":"1.0","source":{"id":"1205.0142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0142","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0142v2","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0142","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"pith_short_12","alias_value":"6KDXIVFQE2ZF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6KDXIVFQE2ZFMSFQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6KDXIVFQ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:5172b5a1b9695cba6aad942abda3eb36005336931eff3892ec17b461483204e8","target":"graph","created_at":"2026-05-18T03:56:23Z","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":"Let M be a smooth strictly convex closed surface in space and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths. In this note we prove that if H is either a closed surface containing M or a plane then M is an Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different.","authors_text":"G. Ruiz-Hernandez, J. Jeronimo-Castro, S. Tabachnikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-01T11:38:04Z","title":"The equal tangents property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0142","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":"sha256:5b3fcf487ed80fa03584e29c5c235795901c829f5741bafdc568a0877d99fa4c","target":"record","created_at":"2026-05-18T03:56:23Z","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":"1f4027798ba89302a06743a8851cfbe3aaa661a080b49921a69f2031ba444eab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-01T11:38:04Z","title_canon_sha256":"1d7e4b8584580ed32f2c308338fc4b3fc35682dc36f95dd249270dd1cd99d23b"},"schema_version":"1.0","source":{"id":"1205.0142","kind":"arxiv","version":2}},"canonical_sha256":"f2877454b026b25648b0effe3077e22a10249b6101c499b21e27749c1ce68106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2877454b026b25648b0effe3077e22a10249b6101c499b21e27749c1ce68106","first_computed_at":"2026-05-18T03:56:23.896909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:23.896909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GBtzjM2SkX4kH3/qbWo5mBf0gcIwBazkZbnbBNDKTv5xMnCs3gfqWP7sfFxPDnQMIOJ9Eq96GwR7VseALi1PBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:23.897580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b3fcf487ed80fa03584e29c5c235795901c829f5741bafdc568a0877d99fa4c","sha256:5172b5a1b9695cba6aad942abda3eb36005336931eff3892ec17b461483204e8"],"state_sha256":"c31e73d977795567c0682b138f2fceaedb53eb1b0355ab7bac8494fe4b34aef5"}