{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FSZGU3DLW3WVDABA3WL6AQHNT2","short_pith_number":"pith:FSZGU3DL","schema_version":"1.0","canonical_sha256":"2cb26a6c6bb6ed518020dd97e040ed9e9f7c98ac50cd34d897cedba6233976de","source":{"kind":"arxiv","id":"1109.5890","version":2},"attestation_state":"computed","paper":{"title":"Analysis of a method to parameterize planar curves immersed in triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.NA","authors_text":"Adrian J. Lew, Ramsharan Rangarajan","submitted_at":"2011-09-16T19:27:39Z","abstract_excerpt":"We prove that a planar $C^2$-regular boundary $\\Gamma$ can always be parameterized with its closest point projection $\\pi$ over a certain collection of edges $\\Gamma_h$ in an ambient triangulation, by making simple assumptions on the background mesh. For $\\Gamma_h$, we select the edges that have both vertices on one side of $\\Gamma$ and belong to a triangle that has a vertex on the other side. By imposing restrictions on the size of triangles near the curve and by requesting that certain angles in the mesh be strictly acute, we prove that $\\pi:\\Gamma_h\\rightarrow\\Gamma$ is a homeomorphism, tha"},"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":"1109.5890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-16T19:27:39Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"91d712e3168b8a8225f8128224c73482444a1f3bdb441e06b97cd45029633a6e","abstract_canon_sha256":"43dae8b4e73da36c968a85ae6b3d4eace1289794c730ffb426935502c00aff66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:26.545722Z","signature_b64":"jN+JFkCcRlpPdErk3QgT/7oxBd8Nd/bVEYZ/PlomfkvrX5OYn5HlUTDVp/NHac4V6F71JI+scWgpD4PLb8EHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cb26a6c6bb6ed518020dd97e040ed9e9f7c98ac50cd34d897cedba6233976de","last_reissued_at":"2026-05-18T03:33:26.545035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:26.545035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of a method to parameterize planar curves immersed in triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.NA","authors_text":"Adrian J. Lew, Ramsharan Rangarajan","submitted_at":"2011-09-16T19:27:39Z","abstract_excerpt":"We prove that a planar $C^2$-regular boundary $\\Gamma$ can always be parameterized with its closest point projection $\\pi$ over a certain collection of edges $\\Gamma_h$ in an ambient triangulation, by making simple assumptions on the background mesh. For $\\Gamma_h$, we select the edges that have both vertices on one side of $\\Gamma$ and belong to a triangle that has a vertex on the other side. By imposing restrictions on the size of triangles near the curve and by requesting that certain angles in the mesh be strictly acute, we prove that $\\pi:\\Gamma_h\\rightarrow\\Gamma$ is a homeomorphism, tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5890","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":"1109.5890","created_at":"2026-05-18T03:33:26.545153+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5890v2","created_at":"2026-05-18T03:33:26.545153+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5890","created_at":"2026-05-18T03:33:26.545153+00:00"},{"alias_kind":"pith_short_12","alias_value":"FSZGU3DLW3WV","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FSZGU3DLW3WVDABA","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FSZGU3DL","created_at":"2026-05-18T12:26:28.662955+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/FSZGU3DLW3WVDABA3WL6AQHNT2","json":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2.json","graph_json":"https://pith.science/api/pith-number/FSZGU3DLW3WVDABA3WL6AQHNT2/graph.json","events_json":"https://pith.science/api/pith-number/FSZGU3DLW3WVDABA3WL6AQHNT2/events.json","paper":"https://pith.science/paper/FSZGU3DL"},"agent_actions":{"view_html":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2","download_json":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2.json","view_paper":"https://pith.science/paper/FSZGU3DL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5890&json=true","fetch_graph":"https://pith.science/api/pith-number/FSZGU3DLW3WVDABA3WL6AQHNT2/graph.json","fetch_events":"https://pith.science/api/pith-number/FSZGU3DLW3WVDABA3WL6AQHNT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2/action/storage_attestation","attest_author":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2/action/author_attestation","sign_citation":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2/action/citation_signature","submit_replication":"https://pith.science/pith/FSZGU3DLW3WVDABA3WL6AQHNT2/action/replication_record"}},"created_at":"2026-05-18T03:33:26.545153+00:00","updated_at":"2026-05-18T03:33:26.545153+00:00"}