{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PMCXNSAAG3B2B5ESLQ4RXUR4P7","short_pith_number":"pith:PMCXNSAA","schema_version":"1.0","canonical_sha256":"7b0576c80036c3a0f4925c391bd23c7ffad28b19402d69d34b46185c0b929725","source":{"kind":"arxiv","id":"1608.01651","version":2},"attestation_state":"computed","paper":{"title":"Closed Cycloids in a Normed Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marcos Craizer, Ralph Teixeira, Vitor Balestro","submitted_at":"2016-08-04T19:35:50Z","abstract_excerpt":"Given a normed plane $\\mathcal{P}$, we call $\\mathcal{P}$-cycloids the planar curves which are homothetic to their double $\\mathcal{P}$-evolutes. It turns out that the radius of curvature and the support function of a $\\mathcal{P}$-cycloid satisfy a differential equation of Sturm-Liouville type. By studying this equation we can describe all closed hypocycloids and epicycloids with a given number of cusps. We can also find an orthonormal basis of ${\\mathcal C}^0(S^1)$ with a natural decomposition into symmetric and anti-symmetric functions, which are support functions of symmetric and constant "},"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":"1608.01651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-04T19:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"077f823b52cb4e79b8f9ff8d5e077b423e731b6b0f91fec2a4d51c7c6812cb52","abstract_canon_sha256":"d9feefbc0abecc8dc8874fc404758c06150cec51ddc847de5b93ac6a85ee28c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:34.001204Z","signature_b64":"4rI0IrQcQp/noJfGk7hTMzFIFl/xAArwG6pU1ZAJVbH1y5VEYBYbuAgZlaWjHyLvNZA74hM8LmL7d9BnhzvTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b0576c80036c3a0f4925c391bd23c7ffad28b19402d69d34b46185c0b929725","last_reissued_at":"2026-05-18T00:51:34.000742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:34.000742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed Cycloids in a Normed Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marcos Craizer, Ralph Teixeira, Vitor Balestro","submitted_at":"2016-08-04T19:35:50Z","abstract_excerpt":"Given a normed plane $\\mathcal{P}$, we call $\\mathcal{P}$-cycloids the planar curves which are homothetic to their double $\\mathcal{P}$-evolutes. It turns out that the radius of curvature and the support function of a $\\mathcal{P}$-cycloid satisfy a differential equation of Sturm-Liouville type. By studying this equation we can describe all closed hypocycloids and epicycloids with a given number of cusps. We can also find an orthonormal basis of ${\\mathcal C}^0(S^1)$ with a natural decomposition into symmetric and anti-symmetric functions, which are support functions of symmetric and constant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01651","kind":"arxiv","version":2},"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":"1608.01651","created_at":"2026-05-18T00:51:34.000819+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.01651v2","created_at":"2026-05-18T00:51:34.000819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01651","created_at":"2026-05-18T00:51:34.000819+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMCXNSAAG3B2","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMCXNSAAG3B2B5ES","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMCXNSAA","created_at":"2026-05-18T12:30:39.010887+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/PMCXNSAAG3B2B5ESLQ4RXUR4P7","json":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7.json","graph_json":"https://pith.science/api/pith-number/PMCXNSAAG3B2B5ESLQ4RXUR4P7/graph.json","events_json":"https://pith.science/api/pith-number/PMCXNSAAG3B2B5ESLQ4RXUR4P7/events.json","paper":"https://pith.science/paper/PMCXNSAA"},"agent_actions":{"view_html":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7","download_json":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7.json","view_paper":"https://pith.science/paper/PMCXNSAA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.01651&json=true","fetch_graph":"https://pith.science/api/pith-number/PMCXNSAAG3B2B5ESLQ4RXUR4P7/graph.json","fetch_events":"https://pith.science/api/pith-number/PMCXNSAAG3B2B5ESLQ4RXUR4P7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7/action/storage_attestation","attest_author":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7/action/author_attestation","sign_citation":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7/action/citation_signature","submit_replication":"https://pith.science/pith/PMCXNSAAG3B2B5ESLQ4RXUR4P7/action/replication_record"}},"created_at":"2026-05-18T00:51:34.000819+00:00","updated_at":"2026-05-18T00:51:34.000819+00:00"}