{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KJODFFOOTITEFLSRCSRPO7WRFV","short_pith_number":"pith:KJODFFOO","schema_version":"1.0","canonical_sha256":"525c3295ce9a2642ae5114a2f77ed12d67b42b6796f532caf59543043a979961","source":{"kind":"arxiv","id":"1210.4543","version":1},"attestation_state":"computed","paper":{"title":"Fourier Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christoph Lamm","submitted_at":"2012-10-16T19:59:24Z","abstract_excerpt":"We show that every knot has a checkerbord diagram and that every knot is the closure of a rosette braid. We define Fourier knots of type (n_1, n_2, n_3) as knots which have parametrizations where each coordinate function x_i(t) is a finite Fourier series of length n_i, and conclude that every knot is a Fourier knot of type (1, 1, n) for some natural number n."},"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":"1210.4543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-16T19:59:24Z","cross_cats_sorted":[],"title_canon_sha256":"8f590177112030d17d43e8e8db4a95f05732d96789031dfe0c4808cf131b98db","abstract_canon_sha256":"c67c6019e3b2d210b799078c3dcce40a3cb8ae4387a8ebe183c67d6bd1347c98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:05.661621Z","signature_b64":"cL3Wj2UfZtbgtbGqO2OZGlx0YX0KigTGQQf9dKxIp/qakVamIQbls+t+8nURK5G8Vogyi1FShLWw5/TVD1tBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"525c3295ce9a2642ae5114a2f77ed12d67b42b6796f532caf59543043a979961","last_reissued_at":"2026-05-18T03:43:05.660988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:05.660988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christoph Lamm","submitted_at":"2012-10-16T19:59:24Z","abstract_excerpt":"We show that every knot has a checkerbord diagram and that every knot is the closure of a rosette braid. We define Fourier knots of type (n_1, n_2, n_3) as knots which have parametrizations where each coordinate function x_i(t) is a finite Fourier series of length n_i, and conclude that every knot is a Fourier knot of type (1, 1, n) for some natural number n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4543","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":"1210.4543","created_at":"2026-05-18T03:43:05.661065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4543v1","created_at":"2026-05-18T03:43:05.661065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4543","created_at":"2026-05-18T03:43:05.661065+00:00"},{"alias_kind":"pith_short_12","alias_value":"KJODFFOOTITE","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KJODFFOOTITEFLSR","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KJODFFOO","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.18783","citing_title":"Quasitoric representation of generalized braids","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV","json":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV.json","graph_json":"https://pith.science/api/pith-number/KJODFFOOTITEFLSRCSRPO7WRFV/graph.json","events_json":"https://pith.science/api/pith-number/KJODFFOOTITEFLSRCSRPO7WRFV/events.json","paper":"https://pith.science/paper/KJODFFOO"},"agent_actions":{"view_html":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV","download_json":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV.json","view_paper":"https://pith.science/paper/KJODFFOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4543&json=true","fetch_graph":"https://pith.science/api/pith-number/KJODFFOOTITEFLSRCSRPO7WRFV/graph.json","fetch_events":"https://pith.science/api/pith-number/KJODFFOOTITEFLSRCSRPO7WRFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV/action/storage_attestation","attest_author":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV/action/author_attestation","sign_citation":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV/action/citation_signature","submit_replication":"https://pith.science/pith/KJODFFOOTITEFLSRCSRPO7WRFV/action/replication_record"}},"created_at":"2026-05-18T03:43:05.661065+00:00","updated_at":"2026-05-18T03:43:05.661065+00:00"}