{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ED4XI7FFCCJ6UAACJLYTKPEOXL","short_pith_number":"pith:ED4XI7FF","schema_version":"1.0","canonical_sha256":"20f9747ca51093ea00024af1353c8ebac6acc74e81f5f9966cd4094ef9e44e88","source":{"kind":"arxiv","id":"1703.02581","version":2},"attestation_state":"computed","paper":{"title":"Results on the homotopy type of the spaces of locally convex curves on $S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Em\\'ilia Alves, Nicolau C. Saldanha","submitted_at":"2017-03-07T20:26:23Z","abstract_excerpt":"A curve $\\gamma: [0,1] \\rightarrow S^n$ of class $C^k$ ($k \\geqslant n$) is locally convex if the vectors $\\gamma(t), \\gamma'(t), \\gamma\"(t), \\cdots, \\gamma^{(n)}(t)$ are a positive orthonormal basis to $R^{n+1}$ for all $t \\in [0,1]$. Given an integer $n \\geq 2$ and $Q \\in SO_{n+1}$, let $LS^n(Q)$ be the set of all locally convex curves $\\gamma: [0,1] \\rightarrow S^n$ with fixed initial and final Frenet frame $F_\\gamma(0)=I$ and $F_\\gamma(1)=Q$. Saldanha and Shapiro proved that there are just finitely many non-homeomorphic spaces among $LS^n(Q)$ when $Q$ varies in $SO_{n+1}$ (in particular, a"},"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":"1703.02581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-07T20:26:23Z","cross_cats_sorted":[],"title_canon_sha256":"c14bbfd175ec1f3aa33bd6581bb8a4f2490d29f2f7a3879d2c09567db559e866","abstract_canon_sha256":"e574219ad28ece0aa663fd87fcf590caa18d6a4d32680c2a0eb7dd591589309d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:31.454218Z","signature_b64":"sA/Lt7NnPCwzn1bc93HVmipWf9mueB7UEnvA4hjSCehcgtz9JgwF8nfiEEel6doFQqs6A1Ky2X25SjZTSkMOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20f9747ca51093ea00024af1353c8ebac6acc74e81f5f9966cd4094ef9e44e88","last_reissued_at":"2026-05-18T00:24:31.453656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:31.453656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Results on the homotopy type of the spaces of locally convex curves on $S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Em\\'ilia Alves, Nicolau C. Saldanha","submitted_at":"2017-03-07T20:26:23Z","abstract_excerpt":"A curve $\\gamma: [0,1] \\rightarrow S^n$ of class $C^k$ ($k \\geqslant n$) is locally convex if the vectors $\\gamma(t), \\gamma'(t), \\gamma\"(t), \\cdots, \\gamma^{(n)}(t)$ are a positive orthonormal basis to $R^{n+1}$ for all $t \\in [0,1]$. Given an integer $n \\geq 2$ and $Q \\in SO_{n+1}$, let $LS^n(Q)$ be the set of all locally convex curves $\\gamma: [0,1] \\rightarrow S^n$ with fixed initial and final Frenet frame $F_\\gamma(0)=I$ and $F_\\gamma(1)=Q$. Saldanha and Shapiro proved that there are just finitely many non-homeomorphic spaces among $LS^n(Q)$ when $Q$ varies in $SO_{n+1}$ (in particular, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02581","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":"1703.02581","created_at":"2026-05-18T00:24:31.453740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02581v2","created_at":"2026-05-18T00:24:31.453740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02581","created_at":"2026-05-18T00:24:31.453740+00:00"},{"alias_kind":"pith_short_12","alias_value":"ED4XI7FFCCJ6","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"ED4XI7FFCCJ6UAAC","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"ED4XI7FF","created_at":"2026-05-18T12:31:12.930513+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/ED4XI7FFCCJ6UAACJLYTKPEOXL","json":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL.json","graph_json":"https://pith.science/api/pith-number/ED4XI7FFCCJ6UAACJLYTKPEOXL/graph.json","events_json":"https://pith.science/api/pith-number/ED4XI7FFCCJ6UAACJLYTKPEOXL/events.json","paper":"https://pith.science/paper/ED4XI7FF"},"agent_actions":{"view_html":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL","download_json":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL.json","view_paper":"https://pith.science/paper/ED4XI7FF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02581&json=true","fetch_graph":"https://pith.science/api/pith-number/ED4XI7FFCCJ6UAACJLYTKPEOXL/graph.json","fetch_events":"https://pith.science/api/pith-number/ED4XI7FFCCJ6UAACJLYTKPEOXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL/action/storage_attestation","attest_author":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL/action/author_attestation","sign_citation":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL/action/citation_signature","submit_replication":"https://pith.science/pith/ED4XI7FFCCJ6UAACJLYTKPEOXL/action/replication_record"}},"created_at":"2026-05-18T00:24:31.453740+00:00","updated_at":"2026-05-18T00:24:31.453740+00:00"}