{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2KYLQWVVFS4OSR65ETH5KWMHKF","short_pith_number":"pith:2KYLQWVV","canonical_record":{"source":{"id":"1308.3862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-18T14:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"21b1be60fa2383aec95bc22cd256980e1552dcc0a5552b2a1c7679ffc00a0992","abstract_canon_sha256":"0ee6fcb0822ad21c8355515bc6e6b74eaadbf0980fe9f274053bd96006ddfc05"},"schema_version":"1.0"},"canonical_sha256":"d2b0b85ab52cb8e947dd24cfd5598751591cb7be78089c589a0878982dc6df81","source":{"kind":"arxiv","id":"1308.3862","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3862","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3862v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3862","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"2KYLQWVVFS4O","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2KYLQWVVFS4OSR65","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2KYLQWVV","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2KYLQWVVFS4OSR65ETH5KWMHKF","target":"record","payload":{"canonical_record":{"source":{"id":"1308.3862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-18T14:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"21b1be60fa2383aec95bc22cd256980e1552dcc0a5552b2a1c7679ffc00a0992","abstract_canon_sha256":"0ee6fcb0822ad21c8355515bc6e6b74eaadbf0980fe9f274053bd96006ddfc05"},"schema_version":"1.0"},"canonical_sha256":"d2b0b85ab52cb8e947dd24cfd5598751591cb7be78089c589a0878982dc6df81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.154258Z","signature_b64":"VkmZ0MOGPQA2pu6NPI79OPCmYni+U1XsCa7pjGLaZvlyIkYbtxOhcKrptx3lLz80IuHSojEbto3ukcCKI+pdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2b0b85ab52cb8e947dd24cfd5598751591cb7be78089c589a0878982dc6df81","last_reissued_at":"2026-05-18T02:51:42.153604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.153604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.3862","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zv3reK1/dYlG8jB9v+3uXLuFOihaP5ONxm20qUSOdnn7FKwAY3nVj6nKJFK5kY3ttM7s3ZGZDHrmA0fykh7MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:52:06.343406Z"},"content_sha256":"4774ad57e23df4cebb0a9d7d321273e971b485eb800c223dce8b6b8e5eb5ed96","schema_version":"1.0","event_id":"sha256:4774ad57e23df4cebb0a9d7d321273e971b485eb800c223dce8b6b8e5eb5ed96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2KYLQWVVFS4OSR65ETH5KWMHKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moderate smoothness of most Alexandrov surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Costin Vilcu, Jin-ichi Itoh, Joel Rouyer","submitted_at":"2013-08-18T14:42:39Z","abstract_excerpt":"We show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by $\\kappa$ have no conical points. We use this result to prove that at most points of such surfaces, the lower and the upper Gaussian curvatures are equal to $\\kappa$ and $\\infty$ respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3862","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3r2zTnI4H+oiPrLpg9LE7Mgt8iuA1Pv9zXF3ogHT+KJXih3jVFDkT5wAt5XkseRAmIXf5zlI6pBzJqvnYufcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:52:06.344131Z"},"content_sha256":"0623590b0003a46c795f564c0c29ba6f7cc85b6f894c7aa920e31feb9412f002","schema_version":"1.0","event_id":"sha256:0623590b0003a46c795f564c0c29ba6f7cc85b6f894c7aa920e31feb9412f002"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/bundle.json","state_url":"https://pith.science/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T04:52:06Z","links":{"resolver":"https://pith.science/pith/2KYLQWVVFS4OSR65ETH5KWMHKF","bundle":"https://pith.science/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/bundle.json","state":"https://pith.science/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KYLQWVVFS4OSR65ETH5KWMHKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2KYLQWVVFS4OSR65ETH5KWMHKF","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":"0ee6fcb0822ad21c8355515bc6e6b74eaadbf0980fe9f274053bd96006ddfc05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-18T14:42:39Z","title_canon_sha256":"21b1be60fa2383aec95bc22cd256980e1552dcc0a5552b2a1c7679ffc00a0992"},"schema_version":"1.0","source":{"id":"1308.3862","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3862","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3862v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3862","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"2KYLQWVVFS4O","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2KYLQWVVFS4OSR65","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2KYLQWVV","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0623590b0003a46c795f564c0c29ba6f7cc85b6f894c7aa920e31feb9412f002","target":"graph","created_at":"2026-05-18T02:51:42Z","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 show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by $\\kappa$ have no conical points. We use this result to prove that at most points of such surfaces, the lower and the upper Gaussian curvatures are equal to $\\kappa$ and $\\infty$ respectively.","authors_text":"Costin Vilcu, Jin-ichi Itoh, Joel Rouyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-18T14:42:39Z","title":"Moderate smoothness of most Alexandrov surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3862","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":"sha256:4774ad57e23df4cebb0a9d7d321273e971b485eb800c223dce8b6b8e5eb5ed96","target":"record","created_at":"2026-05-18T02:51:42Z","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":"0ee6fcb0822ad21c8355515bc6e6b74eaadbf0980fe9f274053bd96006ddfc05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-18T14:42:39Z","title_canon_sha256":"21b1be60fa2383aec95bc22cd256980e1552dcc0a5552b2a1c7679ffc00a0992"},"schema_version":"1.0","source":{"id":"1308.3862","kind":"arxiv","version":2}},"canonical_sha256":"d2b0b85ab52cb8e947dd24cfd5598751591cb7be78089c589a0878982dc6df81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2b0b85ab52cb8e947dd24cfd5598751591cb7be78089c589a0878982dc6df81","first_computed_at":"2026-05-18T02:51:42.153604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.153604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VkmZ0MOGPQA2pu6NPI79OPCmYni+U1XsCa7pjGLaZvlyIkYbtxOhcKrptx3lLz80IuHSojEbto3ukcCKI+pdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.154258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3862","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4774ad57e23df4cebb0a9d7d321273e971b485eb800c223dce8b6b8e5eb5ed96","sha256:0623590b0003a46c795f564c0c29ba6f7cc85b6f894c7aa920e31feb9412f002"],"state_sha256":"3e49ddf080abd633acce839440ec1ebbb0f313f7865d8024848adcf783d52465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6YY8zw4ipV4WfRZ4dmd/70yx6mhM1twweaKBYTZp2LEVry3iK65v47X82XPFnvczaqEfNao46bkpDdb+sGYCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:52:06.347645Z","bundle_sha256":"98914ad44b7c40ad0e6bbeaad3718d1340fe440a072fa79638388ce321679f71"}}