{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VGFRYUJMDRAUMZNDK6HE34XIMQ","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":"3847ad3b6ce187d71227937c44e44eb3f1f430d88e6365860fd59b02c405f99c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-09T10:36:21Z","title_canon_sha256":"bdbc972532601eb827ff7687f199cc5fe1aa4817b5d5dd0233cf20e28b28c282"},"schema_version":"1.0","source":{"id":"1409.2671","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2671","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2671v3","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2671","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"VGFRYUJMDRAU","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VGFRYUJMDRAUMZND","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VGFRYUJM","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:5edcb2a50a7b75e8ff3b41f3e901315653a66ec6e9a2089512ea68bcb9686ff4","target":"graph","created_at":"2026-05-18T01:09:49Z","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":"This paper deals with the merging problem of segments of a composite B\\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P. Wo\\'zny, S. Lewanowicz, Comput. Aided Geom. Design 26 (2009), 566--579) to compute the control points of the merged curve. Thanks to using fast schemes of evaluation of certain connections involving Bernstein and dual Bernstein polynomials, the complexity of our algorithm is significantly less than complexity of other merging methods.","authors_text":"Pawe{\\l} Wo\\'zny, Przemys{\\l}aw Gospodarczyk, Stanis{\\l}aw Lewanowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-09T10:36:21Z","title":"Efficient merging of multiple segments of B\\'ezier curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2671","kind":"arxiv","version":3},"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:ac097d6cf7d553e6c07dd858ab8187a2c7517ba330df3bbae71f8f02532457e1","target":"record","created_at":"2026-05-18T01:09:49Z","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":"3847ad3b6ce187d71227937c44e44eb3f1f430d88e6365860fd59b02c405f99c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-09T10:36:21Z","title_canon_sha256":"bdbc972532601eb827ff7687f199cc5fe1aa4817b5d5dd0233cf20e28b28c282"},"schema_version":"1.0","source":{"id":"1409.2671","kind":"arxiv","version":3}},"canonical_sha256":"a98b1c512c1c414665a3578e4df2e8640fcc2c89919249a19a072f23ffcaa193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a98b1c512c1c414665a3578e4df2e8640fcc2c89919249a19a072f23ffcaa193","first_computed_at":"2026-05-18T01:09:49.703929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:49.703929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKl68wMHpD1bcIHmzptVW1cBBbkmiGiSBD67jFUt6P3XYJUpoz0DhMWrmWJSh5opCznpScXO4AQ6AIYejVc0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:49.704512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2671","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac097d6cf7d553e6c07dd858ab8187a2c7517ba330df3bbae71f8f02532457e1","sha256:5edcb2a50a7b75e8ff3b41f3e901315653a66ec6e9a2089512ea68bcb9686ff4"],"state_sha256":"1d345d0e0e356cdce4e30311b9d252f0da6e7d81f43d5e003f22b42a47604602"}