{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NU6CIQHXOLZ2ZIEZX5HVIA4YVY","short_pith_number":"pith:NU6CIQHX","canonical_record":{"source":{"id":"1603.03959","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-12T19:59:49Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"1fabfe77341cb4bc69602b9a04644e6b500e33aaa6ee1c72fdcdbd2c6c0bd528","abstract_canon_sha256":"271b70d497abf28b166632691ddc8e8f8665115cc9de50d22a9909233ba9642c"},"schema_version":"1.0"},"canonical_sha256":"6d3c2440f772f3aca099bf4f540398ae35926050baef1b555fb99e6a1f50fbe8","source":{"kind":"arxiv","id":"1603.03959","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03959","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03959v3","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03959","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"pith_short_12","alias_value":"NU6CIQHXOLZ2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NU6CIQHXOLZ2ZIEZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NU6CIQHX","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NU6CIQHXOLZ2ZIEZX5HVIA4YVY","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03959","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-12T19:59:49Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"1fabfe77341cb4bc69602b9a04644e6b500e33aaa6ee1c72fdcdbd2c6c0bd528","abstract_canon_sha256":"271b70d497abf28b166632691ddc8e8f8665115cc9de50d22a9909233ba9642c"},"schema_version":"1.0"},"canonical_sha256":"6d3c2440f772f3aca099bf4f540398ae35926050baef1b555fb99e6a1f50fbe8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:39.999612Z","signature_b64":"5dowb0UGJaqhXk8SJCDWaAknDkznAS2kdqmYh7mqG+FSHeagv0Mipip4xC1dEy+7zNjrv7AZh4ZQTWUru9R7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d3c2440f772f3aca099bf4f540398ae35926050baef1b555fb99e6a1f50fbe8","last_reissued_at":"2026-05-18T00:24:39.999131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:39.999131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03959","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":"2026-05-18T00:24:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qo0HwS4U4rn9mt6JUIs/wXrMCubT0WQp1jwP4qsjpEND1CCeo1pxNZAtwNQYBT/gJnCnI/df9K7HPVSOoUy2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:23:40.144397Z"},"content_sha256":"8318919cd601076ef7e572f6de7a62dcb113d9f506524a3c657c911a242683f1","schema_version":"1.0","event_id":"sha256:8318919cd601076ef7e572f6de7a62dcb113d9f506524a3c657c911a242683f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NU6CIQHXOLZ2ZIEZX5HVIA4YVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the computation of the straight lines contained in a rational surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Jorge Caravantes, Juan Gerardo Alc\\'azar","submitted_at":"2016-03-12T19:59:49Z","abstract_excerpt":"In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that characterizes real straight lines contained in a surface as curves that are simultaneously asymptotic lines, and geodesics. We also report on an implementation carried out in Maple 18, and we compare the behavior of our algorithm with two brute-force approaches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03959","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":"2026-05-18T00:24:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5jGOnMJX1alwq4dEpsbzUKoP7GpYRjpuYH4+NWvEuU4WMoENrM/wmtb+cyNGKNFEvTbJbGkhKnTRdNFhrVDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:23:40.144887Z"},"content_sha256":"5c518a238f054369bfb2652f9ba4f8e9a981c109db296fa1fc6ba75af9b2fe8c","schema_version":"1.0","event_id":"sha256:5c518a238f054369bfb2652f9ba4f8e9a981c109db296fa1fc6ba75af9b2fe8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/bundle.json","state_url":"https://pith.science/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/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":"2026-05-26T06:23:40Z","links":{"resolver":"https://pith.science/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY","bundle":"https://pith.science/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/bundle.json","state":"https://pith.science/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NU6CIQHXOLZ2ZIEZX5HVIA4YVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NU6CIQHXOLZ2ZIEZX5HVIA4YVY","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":"271b70d497abf28b166632691ddc8e8f8665115cc9de50d22a9909233ba9642c","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-12T19:59:49Z","title_canon_sha256":"1fabfe77341cb4bc69602b9a04644e6b500e33aaa6ee1c72fdcdbd2c6c0bd528"},"schema_version":"1.0","source":{"id":"1603.03959","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03959","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03959v3","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03959","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"pith_short_12","alias_value":"NU6CIQHXOLZ2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NU6CIQHXOLZ2ZIEZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NU6CIQHX","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:5c518a238f054369bfb2652f9ba4f8e9a981c109db296fa1fc6ba75af9b2fe8c","target":"graph","created_at":"2026-05-18T00:24:39Z","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":"In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that characterizes real straight lines contained in a surface as curves that are simultaneously asymptotic lines, and geodesics. We also report on an implementation carried out in Maple 18, and we compare the behavior of our algorithm with two brute-force approaches.","authors_text":"Jorge Caravantes, Juan Gerardo Alc\\'azar","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-12T19:59:49Z","title":"On the computation of the straight lines contained in a rational surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03959","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":"sha256:8318919cd601076ef7e572f6de7a62dcb113d9f506524a3c657c911a242683f1","target":"record","created_at":"2026-05-18T00:24:39Z","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":"271b70d497abf28b166632691ddc8e8f8665115cc9de50d22a9909233ba9642c","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-12T19:59:49Z","title_canon_sha256":"1fabfe77341cb4bc69602b9a04644e6b500e33aaa6ee1c72fdcdbd2c6c0bd528"},"schema_version":"1.0","source":{"id":"1603.03959","kind":"arxiv","version":3}},"canonical_sha256":"6d3c2440f772f3aca099bf4f540398ae35926050baef1b555fb99e6a1f50fbe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d3c2440f772f3aca099bf4f540398ae35926050baef1b555fb99e6a1f50fbe8","first_computed_at":"2026-05-18T00:24:39.999131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:39.999131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dowb0UGJaqhXk8SJCDWaAknDkznAS2kdqmYh7mqG+FSHeagv0Mipip4xC1dEy+7zNjrv7AZh4ZQTWUru9R7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:39.999612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03959","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8318919cd601076ef7e572f6de7a62dcb113d9f506524a3c657c911a242683f1","sha256:5c518a238f054369bfb2652f9ba4f8e9a981c109db296fa1fc6ba75af9b2fe8c"],"state_sha256":"4903734fa6cb95a708016abb65254489afd2d93574c94fb7dbb5dda58dbc220c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQefvYNoW0nTeolZCN1nUbEtgwYbtYqmqU6SIdKalpyDxEIUq1du6Zck/PX6I1AFv6zhJ7IkkHFBcLtiFxVTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:23:40.148491Z","bundle_sha256":"c157e71869f7024d355cae22b87170cf3638fce414136334458770faf60925ea"}}