{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OMWKEHMOHV7QH2XV33NC5JLECK","short_pith_number":"pith:OMWKEHMO","canonical_record":{"source":{"id":"1006.4380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-22T21:24:31Z","cross_cats_sorted":[],"title_canon_sha256":"eaf99a0ff3a54741ea9649245298faed781a8f6279d9ed9d9d65e4a8a858a5f0","abstract_canon_sha256":"26bc344892f32e72de2dde97990b8443b947b80fd1121513e24027e60a6546a5"},"schema_version":"1.0"},"canonical_sha256":"732ca21d8e3d7f03eaf5deda2ea56412a72e43a37050cbf7e4cd8c405df81838","source":{"kind":"arxiv","id":"1006.4380","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4380","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4380v2","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4380","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"OMWKEHMOHV7Q","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OMWKEHMOHV7QH2XV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OMWKEHMO","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OMWKEHMOHV7QH2XV33NC5JLECK","target":"record","payload":{"canonical_record":{"source":{"id":"1006.4380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-22T21:24:31Z","cross_cats_sorted":[],"title_canon_sha256":"eaf99a0ff3a54741ea9649245298faed781a8f6279d9ed9d9d65e4a8a858a5f0","abstract_canon_sha256":"26bc344892f32e72de2dde97990b8443b947b80fd1121513e24027e60a6546a5"},"schema_version":"1.0"},"canonical_sha256":"732ca21d8e3d7f03eaf5deda2ea56412a72e43a37050cbf7e4cd8c405df81838","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.182757Z","signature_b64":"wGzR8bOQmRoRxtSul+QzCGIXKKp4EWpqGWso9ltdfSGuUFdyNq8Jypu1d3WidRafMTt6OwMJuBKn3Gk2y4LRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"732ca21d8e3d7f03eaf5deda2ea56412a72e43a37050cbf7e4cd8c405df81838","last_reissued_at":"2026-05-18T04:36:51.182102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.182102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.4380","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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2SqVZBqmJ2BfWR0+CdBuSOhHZrvZ6n9J7JcYz1C1vwcxN+Toyf2IW3Nt10z06z2KcMRHOSnUvl/xAdjEIcWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:08:35.584129Z"},"content_sha256":"74147b251240467eef9df3f65f0f770c796eee4bfef181226cead1b0a6f1caab","schema_version":"1.0","event_id":"sha256:74147b251240467eef9df3f65f0f770c796eee4bfef181226cead1b0a6f1caab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OMWKEHMOHV7QH2XV33NC5JLECK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Totally quasi-umbilic timelike surfaces in $\\mathbb{R}^{1,2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeanne N. Clelland","submitted_at":"2010-06-22T21:24:31Z","abstract_excerpt":"For a regular surface in Euclidean space $\\mathbb{R}^3$, umbilic points are precisely the points where the Gauss and mean curvatures $K$ and $H$ satisfy $H^2=K$; moreover, it is well-known that the only totally umbilic surfaces in $\\mathbb{R}^3$ are planes and spheres. But for timelike surfaces in Minkowski space $\\mathbb{R}^{1,2}$, it is possible to have $H^2=K$ at a non-umbilic point; we call such points {\\em quasi-umbilic}, and we give a complete classification of totally quasi-umbilic timelike surfaces in $\\mathbb{R}^{1,2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4380","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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywItLhlYKYvTJRoDFlroyZWDvrGyf5hHxNU04ZZzy+nkeKSsaHn0TC/ML4mTGSAKz36a3TaGilJtWKDHT04sCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:08:35.584491Z"},"content_sha256":"d333144ebd23f6d3042225482560d8f305604c455c27e685fcc99a56eb3cbd80","schema_version":"1.0","event_id":"sha256:d333144ebd23f6d3042225482560d8f305604c455c27e685fcc99a56eb3cbd80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMWKEHMOHV7QH2XV33NC5JLECK/bundle.json","state_url":"https://pith.science/pith/OMWKEHMOHV7QH2XV33NC5JLECK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMWKEHMOHV7QH2XV33NC5JLECK/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":"2026-06-22T14:08:35Z","links":{"resolver":"https://pith.science/pith/OMWKEHMOHV7QH2XV33NC5JLECK","bundle":"https://pith.science/pith/OMWKEHMOHV7QH2XV33NC5JLECK/bundle.json","state":"https://pith.science/pith/OMWKEHMOHV7QH2XV33NC5JLECK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMWKEHMOHV7QH2XV33NC5JLECK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OMWKEHMOHV7QH2XV33NC5JLECK","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":"26bc344892f32e72de2dde97990b8443b947b80fd1121513e24027e60a6546a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-22T21:24:31Z","title_canon_sha256":"eaf99a0ff3a54741ea9649245298faed781a8f6279d9ed9d9d65e4a8a858a5f0"},"schema_version":"1.0","source":{"id":"1006.4380","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4380","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4380v2","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4380","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"OMWKEHMOHV7Q","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OMWKEHMOHV7QH2XV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OMWKEHMO","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:d333144ebd23f6d3042225482560d8f305604c455c27e685fcc99a56eb3cbd80","target":"graph","created_at":"2026-05-18T04:36:51Z","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":"For a regular surface in Euclidean space $\\mathbb{R}^3$, umbilic points are precisely the points where the Gauss and mean curvatures $K$ and $H$ satisfy $H^2=K$; moreover, it is well-known that the only totally umbilic surfaces in $\\mathbb{R}^3$ are planes and spheres. But for timelike surfaces in Minkowski space $\\mathbb{R}^{1,2}$, it is possible to have $H^2=K$ at a non-umbilic point; we call such points {\\em quasi-umbilic}, and we give a complete classification of totally quasi-umbilic timelike surfaces in $\\mathbb{R}^{1,2}$.","authors_text":"Jeanne N. Clelland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-22T21:24:31Z","title":"Totally quasi-umbilic timelike surfaces in $\\mathbb{R}^{1,2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4380","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":"sha256:74147b251240467eef9df3f65f0f770c796eee4bfef181226cead1b0a6f1caab","target":"record","created_at":"2026-05-18T04:36:51Z","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":"26bc344892f32e72de2dde97990b8443b947b80fd1121513e24027e60a6546a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-22T21:24:31Z","title_canon_sha256":"eaf99a0ff3a54741ea9649245298faed781a8f6279d9ed9d9d65e4a8a858a5f0"},"schema_version":"1.0","source":{"id":"1006.4380","kind":"arxiv","version":2}},"canonical_sha256":"732ca21d8e3d7f03eaf5deda2ea56412a72e43a37050cbf7e4cd8c405df81838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"732ca21d8e3d7f03eaf5deda2ea56412a72e43a37050cbf7e4cd8c405df81838","first_computed_at":"2026-05-18T04:36:51.182102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.182102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGzR8bOQmRoRxtSul+QzCGIXKKp4EWpqGWso9ltdfSGuUFdyNq8Jypu1d3WidRafMTt6OwMJuBKn3Gk2y4LRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.182757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4380","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74147b251240467eef9df3f65f0f770c796eee4bfef181226cead1b0a6f1caab","sha256:d333144ebd23f6d3042225482560d8f305604c455c27e685fcc99a56eb3cbd80"],"state_sha256":"566de9c29fb2f9eded170becedcd3073f12a256b473225481adb5adcb469469d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/XMLH8e92blhfnuErHnM9PH6MBymu8edUW84yK4FaPuabLM8zxoEJGpnGKoBILr8x91Yg/lUY4As5zthxmHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:08:35.586443Z","bundle_sha256":"2582e47c4bec2b6dcc81e01f9480e93581a0dbbfa3d4c46e037b737298f95e66"}}