{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IH62QBXYSJVKYHTSCBU56OSLXH","short_pith_number":"pith:IH62QBXY","schema_version":"1.0","canonical_sha256":"41fda806f8926aac1e721069df3a4bb9d8f380935983a60aee2420b900a196d2","source":{"kind":"arxiv","id":"1604.07008","version":1},"attestation_state":"computed","paper":{"title":"A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Alessandra Sestini, Carlotta Giannelli, Caterina Stoppato, Graziano Gentili, Rida T. Farouki","submitted_at":"2016-04-24T10:09:34Z","abstract_excerpt":"A rotation-minimizing frame $({\\bf f}_1,{\\bf f}_2,{\\bf f}_3)$ on a space curve ${\\bf r}(\\xi)$ defines an orthonormal basis for $\\mathbb{R}^3$ in which ${\\bf f}_1={\\bf r}'/|{\\bf r}'|$ is the curve tangent, and the normal-plane vectors ${\\bf f}_2$, ${\\bf f}_3$ exhibit no instantaneous rotation about ${\\bf f}_1$. Polynomial curves that admit rational rotation-minimizing frames (or RRMF curves) form a subset of the Pythagorean-hodograph (PH) curves, specified by integrating the form ${\\bf r}'(\\xi)={\\cal A}(\\xi)\\,{\\bf i}\\,{\\cal A}^*(\\xi)$ for some quaternion polynomial ${\\cal A}(\\xi)$. By introduci"},"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":"1604.07008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-24T10:09:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"832f595642c55df153ab733744a247a400b9369a7a9cafd662330c63f27df057","abstract_canon_sha256":"5f7a74f5523bc3fcb6c1f428623ba2990636268c70520a853eb4b22c1488a939"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:42.865006Z","signature_b64":"oHG28RQhkeUqvQSZUg/VscsQv54zVzAppmYC6aO56ByrzG3w1rxPc7nv9tZRG0edgRWhI4lIO5/FUVOV5GTHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41fda806f8926aac1e721069df3a4bb9d8f380935983a60aee2420b900a196d2","last_reissued_at":"2026-05-18T00:48:42.864255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:42.864255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Alessandra Sestini, Carlotta Giannelli, Caterina Stoppato, Graziano Gentili, Rida T. Farouki","submitted_at":"2016-04-24T10:09:34Z","abstract_excerpt":"A rotation-minimizing frame $({\\bf f}_1,{\\bf f}_2,{\\bf f}_3)$ on a space curve ${\\bf r}(\\xi)$ defines an orthonormal basis for $\\mathbb{R}^3$ in which ${\\bf f}_1={\\bf r}'/|{\\bf r}'|$ is the curve tangent, and the normal-plane vectors ${\\bf f}_2$, ${\\bf f}_3$ exhibit no instantaneous rotation about ${\\bf f}_1$. Polynomial curves that admit rational rotation-minimizing frames (or RRMF curves) form a subset of the Pythagorean-hodograph (PH) curves, specified by integrating the form ${\\bf r}'(\\xi)={\\cal A}(\\xi)\\,{\\bf i}\\,{\\cal A}^*(\\xi)$ for some quaternion polynomial ${\\cal A}(\\xi)$. By introduci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07008","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.07008","created_at":"2026-05-18T00:48:42.864365+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07008v1","created_at":"2026-05-18T00:48:42.864365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07008","created_at":"2026-05-18T00:48:42.864365+00:00"},{"alias_kind":"pith_short_12","alias_value":"IH62QBXYSJVK","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IH62QBXYSJVKYHTS","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IH62QBXY","created_at":"2026-05-18T12:30:22.444734+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/IH62QBXYSJVKYHTSCBU56OSLXH","json":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH.json","graph_json":"https://pith.science/api/pith-number/IH62QBXYSJVKYHTSCBU56OSLXH/graph.json","events_json":"https://pith.science/api/pith-number/IH62QBXYSJVKYHTSCBU56OSLXH/events.json","paper":"https://pith.science/paper/IH62QBXY"},"agent_actions":{"view_html":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH","download_json":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH.json","view_paper":"https://pith.science/paper/IH62QBXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07008&json=true","fetch_graph":"https://pith.science/api/pith-number/IH62QBXYSJVKYHTSCBU56OSLXH/graph.json","fetch_events":"https://pith.science/api/pith-number/IH62QBXYSJVKYHTSCBU56OSLXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH/action/storage_attestation","attest_author":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH/action/author_attestation","sign_citation":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH/action/citation_signature","submit_replication":"https://pith.science/pith/IH62QBXYSJVKYHTSCBU56OSLXH/action/replication_record"}},"created_at":"2026-05-18T00:48:42.864365+00:00","updated_at":"2026-05-18T00:48:42.864365+00:00"}