{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N7H6PX4GEDTPOQLPISWXBGF43C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a87e2f818c3e52dcd8da4147b1793b58fa50e3671f039a6d3c0bf90774de7d83","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-14T02:56:30Z","title_canon_sha256":"cd251a359ee9fa0a9090d4155b508c82819e8183ead728f51a1f401468ca1af8"},"schema_version":"1.0","source":{"id":"1212.3385","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3385","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3385v4","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3385","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"N7H6PX4GEDTP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N7H6PX4GEDTPOQLP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N7H6PX4G","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:c18beb22f7008af78259ee89ee43672748c41940bcbb0b77523947533aae36df","target":"graph","created_at":"2026-05-18T02:42:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we propose a method to obtain a constrained approximation of a rational B\\'{e}zier curve by a polynomial B\\'{e}zier curve. This problem is reformulated as an approximation problem between two polynomial B\\'{e}zier curves based on weighted least-squares method, where weight functions $\\rho(t)=\\omega(t)$ and $\\rho(t)=\\omega(t)^{2}$ are studied respectively. The efficiency of the proposed method is tested using some examples.","authors_text":"Jiansong Deng, Mao Shi","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-14T02:56:30Z","title":"Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3385","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2b0a7871ed998de0a0938c0c1bfc93fb68eb975c5827980c2e941bb06ef4aa79","target":"record","created_at":"2026-05-18T02:42:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a87e2f818c3e52dcd8da4147b1793b58fa50e3671f039a6d3c0bf90774de7d83","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-14T02:56:30Z","title_canon_sha256":"cd251a359ee9fa0a9090d4155b508c82819e8183ead728f51a1f401468ca1af8"},"schema_version":"1.0","source":{"id":"1212.3385","kind":"arxiv","version":4}},"canonical_sha256":"6fcfe7df8620e6f7416f44ad7098bcd8bfe039f89ee7ba41ac7e06123d2ebdd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fcfe7df8620e6f7416f44ad7098bcd8bfe039f89ee7ba41ac7e06123d2ebdd8","first_computed_at":"2026-05-18T02:42:54.220545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:54.220545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBzbOZ2vMC5Tkz/0gsf4NkTKAfU+xA9+8UlQEq0n58jzjcfDDb3HCy+R8csXTS0aU6ibo0+NTeR/vD5Tvb//CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:54.220915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3385","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b0a7871ed998de0a0938c0c1bfc93fb68eb975c5827980c2e941bb06ef4aa79","sha256:c18beb22f7008af78259ee89ee43672748c41940bcbb0b77523947533aae36df"],"state_sha256":"b4228a9938632d817cc68bd09d5eb0e85c4550468c10dc1ed4bf1c5df0caba78"}