{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ESSTDVKEDE4TRWSRCTMINFJGA7","short_pith_number":"pith:ESSTDVKE","schema_version":"1.0","canonical_sha256":"24a531d544193938da5114d886952607f2896f5b9db2659cba1bf4d74ccdbc06","source":{"kind":"arxiv","id":"1610.04418","version":2},"attestation_state":"computed","paper":{"title":"Lissajous-toric knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Marc Soret, Marina Ville","submitted_at":"2016-10-14T11:54:21Z","abstract_excerpt":"A point in the $(N,q)$-torus knot in $\\mathbb{R}^3$ goes $q$ times along a vertical circle while this circle rotates $N$ times around the vertical axis. In the Lissajous-toric knot $K(N,q,p)$, the point goes along a vertical Lissajous curve (parametrized by $t\\mapsto(\\sin(qt+\\phi),\\cos(pt+\\psi)))$ while this curve rotates $N$ times around the vertical axis. Such a knot has a natural braid representation $B_{N,q,p}$ which we investigate here. If $gcd(q,p)=1$, $K(N,q,p)$ is ribbon; if $gcd(q,p)=d>1$, $B_{N,q,p}$ is the $d$-th power of a braid which closes in a ribbon knot. We give an upper bound"},"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":"1610.04418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-14T11:54:21Z","cross_cats_sorted":[],"title_canon_sha256":"9bc65a468a38eeba21cef23c3ddb7412cd3cbc540a56b4425779ba2b85af1b61","abstract_canon_sha256":"cb772ceba40202a5f3cae93534a867f7641780c884f6fdf13ad1bcf34551b302"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:52.377852Z","signature_b64":"iAgyXojZT1g7qVyqqTqMkSpq0tQloluIgV90cQkEjN5hzyl4lPH7kVQPjRgtfJ5HO7ExMlRfCDxEgSXdHGHlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24a531d544193938da5114d886952607f2896f5b9db2659cba1bf4d74ccdbc06","last_reissued_at":"2026-05-18T01:00:52.377247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:52.377247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lissajous-toric knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Marc Soret, Marina Ville","submitted_at":"2016-10-14T11:54:21Z","abstract_excerpt":"A point in the $(N,q)$-torus knot in $\\mathbb{R}^3$ goes $q$ times along a vertical circle while this circle rotates $N$ times around the vertical axis. In the Lissajous-toric knot $K(N,q,p)$, the point goes along a vertical Lissajous curve (parametrized by $t\\mapsto(\\sin(qt+\\phi),\\cos(pt+\\psi)))$ while this curve rotates $N$ times around the vertical axis. Such a knot has a natural braid representation $B_{N,q,p}$ which we investigate here. If $gcd(q,p)=1$, $K(N,q,p)$ is ribbon; if $gcd(q,p)=d>1$, $B_{N,q,p}$ is the $d$-th power of a braid which closes in a ribbon knot. 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