{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:X3G4WFUILAQ6KEBZLTCZPM5WER","short_pith_number":"pith:X3G4WFUI","canonical_record":{"source":{"id":"1107.1584","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-08T09:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"4d5d8e57fb402e3061ae7c1e5c822978449c9bd7cc12bd4474e5def994bb283d","abstract_canon_sha256":"7af535e260123a8fdbaee5f4e87743b048ecf05f79ddb56b08bdea9c33269f09"},"schema_version":"1.0"},"canonical_sha256":"becdcb16885821e510395cc597b3b624543b6a2f157a5bd512fc83ce75a80889","source":{"kind":"arxiv","id":"1107.1584","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1584","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1584v3","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1584","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"X3G4WFUILAQ6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X3G4WFUILAQ6KEBZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X3G4WFUI","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:X3G4WFUILAQ6KEBZLTCZPM5WER","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1584","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-08T09:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"4d5d8e57fb402e3061ae7c1e5c822978449c9bd7cc12bd4474e5def994bb283d","abstract_canon_sha256":"7af535e260123a8fdbaee5f4e87743b048ecf05f79ddb56b08bdea9c33269f09"},"schema_version":"1.0"},"canonical_sha256":"becdcb16885821e510395cc597b3b624543b6a2f157a5bd512fc83ce75a80889","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:06.457556Z","signature_b64":"BjR8VW20aTDYlsMwJWeONIrv5uGb50nvSdnkw/OXPB3PRffXqSPju+ThTYws5rBWcbuhsi9uRlqsGq+mtP94Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"becdcb16885821e510395cc597b3b624543b6a2f157a5bd512fc83ce75a80889","last_reissued_at":"2026-05-18T03:22:06.456677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:06.456677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1584","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ee1AY0g8OASivnDZrr5r61Ff57jA17bKAhciedcUuLgjOrSy78AC5Iz6c+1CDUOrdTN/PvyAe8J/5sgENkXvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:33:38.315356Z"},"content_sha256":"9d3e76754f87a1a0d067c841618c4fa27d115ed3391045d4540432babdf1f502","schema_version":"1.0","event_id":"sha256:9d3e76754f87a1a0d067c841618c4fa27d115ed3391045d4540432babdf1f502"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:X3G4WFUILAQ6KEBZLTCZPM5WER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Parametrization of Space Algebraic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J. Rafael Sendra, Juana Sendra, Sonia L. Rueda","submitted_at":"2011-07-08T09:27:30Z","abstract_excerpt":"Given a non-rational real space curve and a tolerance $\\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the space curve is $\\epsilon$-rational and, in the affirmative case, generates a planar parametrization that is lifted to an space parametrization. This output rational space curve is of the same degree as the input curve, both have the same structure at infinity, and the Hausdorff distance between them is always finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1584","kind":"arxiv","version":3},"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":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Lv1mQD7TES8J06AWu3gJ+4QbRoziJ1RdFtZKfUypiOcg9WDMztX0bT2nZ2Gf0EFUfdspgHqR5WXUJTGJYFODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:33:38.316012Z"},"content_sha256":"ceb6bf46dbbcaea8e0fa85ac3f10a0acefb8b5a547f1bafb7a8570d8f8b66b3d","schema_version":"1.0","event_id":"sha256:ceb6bf46dbbcaea8e0fa85ac3f10a0acefb8b5a547f1bafb7a8570d8f8b66b3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/bundle.json","state_url":"https://pith.science/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/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":"2026-06-10T22:33:38Z","links":{"resolver":"https://pith.science/pith/X3G4WFUILAQ6KEBZLTCZPM5WER","bundle":"https://pith.science/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/bundle.json","state":"https://pith.science/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3G4WFUILAQ6KEBZLTCZPM5WER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:X3G4WFUILAQ6KEBZLTCZPM5WER","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":"7af535e260123a8fdbaee5f4e87743b048ecf05f79ddb56b08bdea9c33269f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-08T09:27:30Z","title_canon_sha256":"4d5d8e57fb402e3061ae7c1e5c822978449c9bd7cc12bd4474e5def994bb283d"},"schema_version":"1.0","source":{"id":"1107.1584","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1584","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1584v3","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1584","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"X3G4WFUILAQ6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X3G4WFUILAQ6KEBZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X3G4WFUI","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:ceb6bf46dbbcaea8e0fa85ac3f10a0acefb8b5a547f1bafb7a8570d8f8b66b3d","target":"graph","created_at":"2026-05-18T03:22:06Z","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":"Given a non-rational real space curve and a tolerance $\\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the space curve is $\\epsilon$-rational and, in the affirmative case, generates a planar parametrization that is lifted to an space parametrization. This output rational space curve is of the same degree as the input curve, both have the same structure at infinity, and the Hausdorff distance between them is always finite.","authors_text":"J. Rafael Sendra, Juana Sendra, Sonia L. Rueda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-08T09:27:30Z","title":"Approximate Parametrization of Space Algebraic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1584","kind":"arxiv","version":3},"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":"sha256:9d3e76754f87a1a0d067c841618c4fa27d115ed3391045d4540432babdf1f502","target":"record","created_at":"2026-05-18T03:22:06Z","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":"7af535e260123a8fdbaee5f4e87743b048ecf05f79ddb56b08bdea9c33269f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-08T09:27:30Z","title_canon_sha256":"4d5d8e57fb402e3061ae7c1e5c822978449c9bd7cc12bd4474e5def994bb283d"},"schema_version":"1.0","source":{"id":"1107.1584","kind":"arxiv","version":3}},"canonical_sha256":"becdcb16885821e510395cc597b3b624543b6a2f157a5bd512fc83ce75a80889","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"becdcb16885821e510395cc597b3b624543b6a2f157a5bd512fc83ce75a80889","first_computed_at":"2026-05-18T03:22:06.456677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:06.456677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BjR8VW20aTDYlsMwJWeONIrv5uGb50nvSdnkw/OXPB3PRffXqSPju+ThTYws5rBWcbuhsi9uRlqsGq+mtP94Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:06.457556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1584","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d3e76754f87a1a0d067c841618c4fa27d115ed3391045d4540432babdf1f502","sha256:ceb6bf46dbbcaea8e0fa85ac3f10a0acefb8b5a547f1bafb7a8570d8f8b66b3d"],"state_sha256":"971126d525a6fb88941de419518216802fd01942c587a077fc06078621533618"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2vsu3ZQWD1vn5mzyfKcAX0MKtinV7vi0lS40tlXQzILmaDCq6C/EbTM/Na2dPS+vBzTlrPS61+JgaNjzqgBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:33:38.320074Z","bundle_sha256":"5b815b1dc427915f619ea8a6d0389bfa191d2bc244b591258bc36d063609cb04"}}