{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SMZMR64TJFSAALUXXXMKE44LYM","short_pith_number":"pith:SMZMR64T","schema_version":"1.0","canonical_sha256":"9332c8fb934964002e97bdd8a2738bc310812caab6515f7ad6ad7260d2a1f515","source":{"kind":"arxiv","id":"1502.04518","version":3},"attestation_state":"computed","paper":{"title":"A new method to compute the singularities of offsets to rational plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gema M. Diaz-Toca, Jorge Caravantes, Juan Gerardo Alc\\'azar","submitted_at":"2015-02-16T12:58:40Z","abstract_excerpt":"Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Mapl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.04518","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-16T12:58:40Z","cross_cats_sorted":[],"title_canon_sha256":"4d9cb8dbd0f83a41bae44e19d8c9af32f686bacfe3db4f9bc693c6bc3b033838","abstract_canon_sha256":"b2083450b92f0cb6bfb5d937db978ab14182fed7d743e130fc4a6695f4c0a2ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:08.824862Z","signature_b64":"NHEHY3YZ7PLPf8inbcbgpDe+XTS8T9MDPGh38R+NTj0AUfD0MtL7t/zrI+lQbVEB9QOiskcIzPJKB8+DJKWxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9332c8fb934964002e97bdd8a2738bc310812caab6515f7ad6ad7260d2a1f515","last_reissued_at":"2026-05-18T01:53:08.824428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:08.824428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new method to compute the singularities of offsets to rational plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gema M. Diaz-Toca, Jorge Caravantes, Juan Gerardo Alc\\'azar","submitted_at":"2015-02-16T12:58:40Z","abstract_excerpt":"Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Mapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04518","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.04518","created_at":"2026-05-18T01:53:08.824493+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04518v3","created_at":"2026-05-18T01:53:08.824493+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04518","created_at":"2026-05-18T01:53:08.824493+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMZMR64TJFSA","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMZMR64TJFSAALUX","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMZMR64T","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM","json":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM.json","graph_json":"https://pith.science/api/pith-number/SMZMR64TJFSAALUXXXMKE44LYM/graph.json","events_json":"https://pith.science/api/pith-number/SMZMR64TJFSAALUXXXMKE44LYM/events.json","paper":"https://pith.science/paper/SMZMR64T"},"agent_actions":{"view_html":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM","download_json":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM.json","view_paper":"https://pith.science/paper/SMZMR64T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04518&json=true","fetch_graph":"https://pith.science/api/pith-number/SMZMR64TJFSAALUXXXMKE44LYM/graph.json","fetch_events":"https://pith.science/api/pith-number/SMZMR64TJFSAALUXXXMKE44LYM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM/action/storage_attestation","attest_author":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM/action/author_attestation","sign_citation":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM/action/citation_signature","submit_replication":"https://pith.science/pith/SMZMR64TJFSAALUXXXMKE44LYM/action/replication_record"}},"created_at":"2026-05-18T01:53:08.824493+00:00","updated_at":"2026-05-18T01:53:08.824493+00:00"}