{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:623FUQQCGC4I6JHRDIYZXWAMWZ","short_pith_number":"pith:623FUQQC","canonical_record":{"source":{"id":"1304.0233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-31T17:17:12Z","cross_cats_sorted":[],"title_canon_sha256":"64da16b05f28dd08691825c4de677faea97aefd97b80adf5bd6846176bcbcd62","abstract_canon_sha256":"f8b8482ebf08dd5b6d48269141f8232061475c08727f1831c76a358d88cd9c53"},"schema_version":"1.0"},"canonical_sha256":"f6b65a420230b88f24f11a319bd80cb64b8ab7405652deb438325d0ac44dd13e","source":{"kind":"arxiv","id":"1304.0233","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0233","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0233v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0233","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"623FUQQCGC4I","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"623FUQQCGC4I6JHR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"623FUQQC","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:623FUQQCGC4I6JHRDIYZXWAMWZ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-31T17:17:12Z","cross_cats_sorted":[],"title_canon_sha256":"64da16b05f28dd08691825c4de677faea97aefd97b80adf5bd6846176bcbcd62","abstract_canon_sha256":"f8b8482ebf08dd5b6d48269141f8232061475c08727f1831c76a358d88cd9c53"},"schema_version":"1.0"},"canonical_sha256":"f6b65a420230b88f24f11a319bd80cb64b8ab7405652deb438325d0ac44dd13e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.610172Z","signature_b64":"jpBOryJLSFZR8BJusl7FsTIrofG0nfZapvrp5lKLvP7yWAlVwZh0gFa+NEfp1d0BGTychGhhlRQcc6lT54GSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b65a420230b88f24f11a319bd80cb64b8ab7405652deb438325d0ac44dd13e","last_reissued_at":"2026-05-18T03:29:25.609447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.609447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0233","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V962sz3OZDo3GiBkYlsiSklJw7w5PWel7mPobIJP1i4o5LeDKmFKSG7tys7XWxAr+am6aIsuqA/11uISsgYYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:44:33.020394Z"},"content_sha256":"f160eb3626bab58b1cd4f17d334487546d15dc1e18129cd3a4f92c0f17ad85df","schema_version":"1.0","event_id":"sha256:f160eb3626bab58b1cd4f17d334487546d15dc1e18129cd3a4f92c0f17ad85df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:623FUQQCGC4I6JHRDIYZXWAMWZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Order Contact on Cayley's Ruled Cubic Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hans Havlicek","submitted_at":"2013-03-31T17:17:12Z","abstract_excerpt":"It is well known that Cayley's ruled cubic surface carries a three-parameter family of twisted cubics sharing a common point, with the same tangent and the same osculating plane. We report on various results and open problems with respect to contact of higher order and dual contact of higher order for these curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0233","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrIRxWQLhCJPnX/37e0Qd50QLWCLsHxXZZtR1xCU3bdG2YFR+67ZAUfQUrcuFpi15IjUTQ5aemjf4PQhaY1KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:44:33.020740Z"},"content_sha256":"8dac71023c8a500ccfa5650594afd6b1f0d2dbec4203231d417452aef5ca306b","schema_version":"1.0","event_id":"sha256:8dac71023c8a500ccfa5650594afd6b1f0d2dbec4203231d417452aef5ca306b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/bundle.json","state_url":"https://pith.science/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/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":"2026-06-24T19:44:33Z","links":{"resolver":"https://pith.science/pith/623FUQQCGC4I6JHRDIYZXWAMWZ","bundle":"https://pith.science/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/bundle.json","state":"https://pith.science/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/623FUQQCGC4I6JHRDIYZXWAMWZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:623FUQQCGC4I6JHRDIYZXWAMWZ","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":"f8b8482ebf08dd5b6d48269141f8232061475c08727f1831c76a358d88cd9c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-31T17:17:12Z","title_canon_sha256":"64da16b05f28dd08691825c4de677faea97aefd97b80adf5bd6846176bcbcd62"},"schema_version":"1.0","source":{"id":"1304.0233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0233","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0233v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0233","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"623FUQQCGC4I","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"623FUQQCGC4I6JHR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"623FUQQC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:8dac71023c8a500ccfa5650594afd6b1f0d2dbec4203231d417452aef5ca306b","target":"graph","created_at":"2026-05-18T03:29:25Z","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":"It is well known that Cayley's ruled cubic surface carries a three-parameter family of twisted cubics sharing a common point, with the same tangent and the same osculating plane. We report on various results and open problems with respect to contact of higher order and dual contact of higher order for these curves.","authors_text":"Hans Havlicek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-31T17:17:12Z","title":"Higher Order Contact on Cayley's Ruled Cubic Surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0233","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:f160eb3626bab58b1cd4f17d334487546d15dc1e18129cd3a4f92c0f17ad85df","target":"record","created_at":"2026-05-18T03:29:25Z","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":"f8b8482ebf08dd5b6d48269141f8232061475c08727f1831c76a358d88cd9c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-31T17:17:12Z","title_canon_sha256":"64da16b05f28dd08691825c4de677faea97aefd97b80adf5bd6846176bcbcd62"},"schema_version":"1.0","source":{"id":"1304.0233","kind":"arxiv","version":1}},"canonical_sha256":"f6b65a420230b88f24f11a319bd80cb64b8ab7405652deb438325d0ac44dd13e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b65a420230b88f24f11a319bd80cb64b8ab7405652deb438325d0ac44dd13e","first_computed_at":"2026-05-18T03:29:25.609447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:25.609447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jpBOryJLSFZR8BJusl7FsTIrofG0nfZapvrp5lKLvP7yWAlVwZh0gFa+NEfp1d0BGTychGhhlRQcc6lT54GSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:25.610172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f160eb3626bab58b1cd4f17d334487546d15dc1e18129cd3a4f92c0f17ad85df","sha256:8dac71023c8a500ccfa5650594afd6b1f0d2dbec4203231d417452aef5ca306b"],"state_sha256":"bc68bebb91df56140b5356fe1609fc8344148e40b85e8d51fce38c7dd1ff73a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUq1L9T9hWLRMjIlzexLVB6DOEAaVrDnTu1YXStfvKZYBVKdmkelypdUsA/sk5QSZnY/TMgXEI4Btbe5LSF2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:44:33.022704Z","bundle_sha256":"73e89e8d1a635fe9eb5dd08c5e942b690d4dac59a0580acea503ff9552877471"}}