{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZWVPSG5SPXVLWPOLJ3FZBEMJEU","short_pith_number":"pith:ZWVPSG5S","schema_version":"1.0","canonical_sha256":"cdaaf91bb27deabb3dcb4ecb9091892515c03bd2ede11f38c00a5924c5d1fede","source":{"kind":"arxiv","id":"1708.04651","version":1},"attestation_state":"computed","paper":{"title":"A relation between the curvature ellipse and the curvature parabola","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pedro Benedini Riul, Ra\\'ul Oset Sinha","submitted_at":"2017-08-15T19:05:37Z","abstract_excerpt":"At each point in an immersed surface in $\\mathbb R^4$ there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. More recently, at the singular point of a corank 1 singular surface in $\\mathbb R^3$, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in $\\mathbb R^4$ to $\\mathbb R^3$ in a tangent direction corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where m"},"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":"1708.04651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-15T19:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"89c1110ae1341798fe614746de1e678dc055afbdfe01fd4e4928c4d283e419fe","abstract_canon_sha256":"22bd580547f7e51ae6a1f371a9710872ba6aa4e53063595a96cf67966ab7873e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:58.333252Z","signature_b64":"F0SKF/Pmuf4D0Xww0+Yv73ZyF6VX7ZzxiESEF5N44TYrkQ9ZpZUmlu/UEd8ZXRs+59tlY4MbVVTR57ieHnkQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdaaf91bb27deabb3dcb4ecb9091892515c03bd2ede11f38c00a5924c5d1fede","last_reissued_at":"2026-05-18T00:37:58.332650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:58.332650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A relation between the curvature ellipse and the curvature parabola","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pedro Benedini Riul, Ra\\'ul Oset Sinha","submitted_at":"2017-08-15T19:05:37Z","abstract_excerpt":"At each point in an immersed surface in $\\mathbb R^4$ there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. More recently, at the singular point of a corank 1 singular surface in $\\mathbb R^3$, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in $\\mathbb R^4$ to $\\mathbb R^3$ in a tangent direction corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04651","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":"1708.04651","created_at":"2026-05-18T00:37:58.332754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04651v1","created_at":"2026-05-18T00:37:58.332754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04651","created_at":"2026-05-18T00:37:58.332754+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZWVPSG5SPXVL","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZWVPSG5SPXVLWPOL","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZWVPSG5S","created_at":"2026-05-18T12:31:59.375834+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/ZWVPSG5SPXVLWPOLJ3FZBEMJEU","json":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU.json","graph_json":"https://pith.science/api/pith-number/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/graph.json","events_json":"https://pith.science/api/pith-number/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/events.json","paper":"https://pith.science/paper/ZWVPSG5S"},"agent_actions":{"view_html":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU","download_json":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU.json","view_paper":"https://pith.science/paper/ZWVPSG5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04651&json=true","fetch_graph":"https://pith.science/api/pith-number/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/action/storage_attestation","attest_author":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/action/author_attestation","sign_citation":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/action/citation_signature","submit_replication":"https://pith.science/pith/ZWVPSG5SPXVLWPOLJ3FZBEMJEU/action/replication_record"}},"created_at":"2026-05-18T00:37:58.332754+00:00","updated_at":"2026-05-18T00:37:58.332754+00:00"}