{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WD2AU3HQTGSR2UPIIFDSWMKPAN","short_pith_number":"pith:WD2AU3HQ","schema_version":"1.0","canonical_sha256":"b0f40a6cf099a51d51e841472b314f03458522830971a2ccd9a730620e6fc352","source":{"kind":"arxiv","id":"2605.13022","version":1},"attestation_state":"computed","paper":{"title":"A necessary condition for cylindrical curves in terms of curvature and torsion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A curve lies on a circular cylinder only if its curvature and torsion satisfy a derived differential equation.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rafael L\\'opez","submitted_at":"2026-05-13T05:25:16Z","abstract_excerpt":"We establish necessary conditions for a regular curve to lie on a circular cylinder in terms of its curvature $\\kappa$ and torsion $\\tau$. By identifying a fundamental function $\\psi = \\sin^2 \\alpha$, representing the squared sine of the angle between the tangent vector and the axis of the cylinder, we reduce the geometric inclusion problem to a compatibility condition between an explicit eighth-degree polynomial equation and a differential equation for $\\psi$. This approach yields a single ODE involving only $\\kappa$ and $\\tau$ that governs the inclusion of the curve in the cylinder. The robu"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.13022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-13T05:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"ee7f4359fc31a21e263252bfc9df06b892e69baba5b653aa704f2ecc02711789","abstract_canon_sha256":"6190bf0d8240c05a6eb7c4e3484ec185848c12a3fbf138c6f834b84d2f9275ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:59.996610Z","signature_b64":"juwIXkWj3h1Ihs3nQ8atqN4K8XiG++fN889uGi2Dc57hmwPHVXd3E/wYOvMzvq8SuwpsH1sAnyqsavNGwWisBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0f40a6cf099a51d51e841472b314f03458522830971a2ccd9a730620e6fc352","last_reissued_at":"2026-05-18T03:08:59.995997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:59.995997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A necessary condition for cylindrical curves in terms of curvature and torsion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A curve lies on a circular cylinder only if its curvature and torsion satisfy a derived differential equation.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rafael L\\'opez","submitted_at":"2026-05-13T05:25:16Z","abstract_excerpt":"We establish necessary conditions for a regular curve to lie on a circular cylinder in terms of its curvature $\\kappa$ and torsion $\\tau$. By identifying a fundamental function $\\psi = \\sin^2 \\alpha$, representing the squared sine of the angle between the tangent vector and the axis of the cylinder, we reduce the geometric inclusion problem to a compatibility condition between an explicit eighth-degree polynomial equation and a differential equation for $\\psi$. This approach yields a single ODE involving only $\\kappa$ and $\\tau$ that governs the inclusion of the curve in the cylinder. The robu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This approach yields a single ODE involving only κ and τ that governs the inclusion of the curve in the cylinder.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The curve is regular (non-vanishing speed) and the cylinder is circular with a well-defined fixed axis so that the angle α between the tangent and the axis is globally consistent along the curve.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A regular curve lies on a circular cylinder only if its curvature κ and torsion τ satisfy a specific compatibility ODE obtained from an eighth-degree polynomial condition on the angle function ψ.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A curve lies on a circular cylinder only if its curvature and torsion satisfy a derived differential equation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d53a78814b6534d8ff420d5aecdd9b86b4d39dabcbeb2fd98ccaac1dc55ddad2"},"source":{"id":"2605.13022","kind":"arxiv","version":1},"verdict":{"id":"8f1d69b3-8e55-4d83-b074-a6766985b516","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T02:20:17.147387Z","strongest_claim":"This approach yields a single ODE involving only κ and τ that governs the inclusion of the curve in the cylinder.","one_line_summary":"A regular curve lies on a circular cylinder only if its curvature κ and torsion τ satisfy a specific compatibility ODE obtained from an eighth-degree polynomial condition on the angle function ψ.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The curve is regular (non-vanishing speed) and the cylinder is circular with a well-defined fixed axis so that the angle α between the tangent and the axis is globally consistent along the curve.","pith_extraction_headline":"A curve lies on a circular cylinder only if its curvature and torsion satisfy a derived differential equation."},"references":{"count":21,"sample":[{"doi":"","year":1975,"title":"R. L. Bishop, There is more than one way to frame a curve. Am. Math. Mon. 82 (1975), 246–251","work_id":"c6d14ed4-d915-4150-8b8a-5be45e4251f3","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"L. C. B. Da Silva, Moving frames and the characterization of curves that lie on a surface. J. Geom. 108 (2017), 1091","work_id":"dd2557d5-444f-40e2-a8f5-18980b375a5a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"L. C. B. Da Silva, J. D. Da Silva, Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere. Mediterr. J. Math. 15 (2018), 70","work_id":"c584a4eb-d3b2-4469-bff0-4c6223ac7ed3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1976,"title":"M. P. Do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ, 1976","work_id":"55b25608-3e88-45fd-b5cd-f337978e63dc","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"D. A. Forsyth, Recognizing algebraic surfaces from their outlines. In: International Conference on Computer Vision, Berlin, pp. 476–480, 1993","work_id":"03d39cbc-d89a-4ada-b942-9d050f593db9","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"581140c3b2511d754a8aa2dfee1c80db5711d289f2f7392009a2a79e6c926f39","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6aa044a6727f458e78018081dc277d6786375e2f89485561644e76f1325928a9"},"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":"2605.13022","created_at":"2026-05-18T03:08:59.996104+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13022v1","created_at":"2026-05-18T03:08:59.996104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13022","created_at":"2026-05-18T03:08:59.996104+00:00"},{"alias_kind":"pith_short_12","alias_value":"WD2AU3HQTGSR","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"WD2AU3HQTGSR2UPI","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"WD2AU3HQ","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN","json":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN.json","graph_json":"https://pith.science/api/pith-number/WD2AU3HQTGSR2UPIIFDSWMKPAN/graph.json","events_json":"https://pith.science/api/pith-number/WD2AU3HQTGSR2UPIIFDSWMKPAN/events.json","paper":"https://pith.science/paper/WD2AU3HQ"},"agent_actions":{"view_html":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN","download_json":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN.json","view_paper":"https://pith.science/paper/WD2AU3HQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13022&json=true","fetch_graph":"https://pith.science/api/pith-number/WD2AU3HQTGSR2UPIIFDSWMKPAN/graph.json","fetch_events":"https://pith.science/api/pith-number/WD2AU3HQTGSR2UPIIFDSWMKPAN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN/action/storage_attestation","attest_author":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN/action/author_attestation","sign_citation":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN/action/citation_signature","submit_replication":"https://pith.science/pith/WD2AU3HQTGSR2UPIIFDSWMKPAN/action/replication_record"}},"created_at":"2026-05-18T03:08:59.996104+00:00","updated_at":"2026-05-18T03:08:59.996104+00:00"}