{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QI6H65AOX3XRYZRLWGK5GSPARF","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":"954136c1e96849f220156929f1c42a6af507396a982d6b5563b10c80db43c8a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T16:51:47Z","title_canon_sha256":"2232d038cad52a79ff96374da9248d473461d5566cee91bbbbea1b15ffdd930a"},"schema_version":"1.0","source":{"id":"1701.03058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03058","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03058v2","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03058","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"QI6H65AOX3XR","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QI6H65AOX3XRYZRL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QI6H65AO","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:a5a9f63d685952d2dd5345ae6091c5e1c66cd4f04dfec067ef0e69354e6b9e36","target":"graph","created_at":"2026-05-18T00:41:37Z","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 the paper, we show that the transformations between modified Jacobi and Bernstein bases of the constrained space of polynomials of degree at most $n$ can be performed with the complexity $O(n^2)$. As a result, the algorithm of degree reduction of B\\'ezier curves that was first presented in (Bhrawy et al., J. Comput. Appl. Math. 302 (2016), 369--384), and then corrected in (Lu and Xiang, J. Comput. Appl. Math. 315 (2017), 65--69), can be significantly improved, since the necessary transformations are done in those papers with the complexity $O(n^3)$. The comparison of running times shows tha","authors_text":"Pawe{\\l} Wo\\'zny, Przemys{\\l}aw Gospodarczyk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T16:51:47Z","title":"Efficient modified Jacobi-Bernstein basis transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03058","kind":"arxiv","version":2},"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":"sha256:75197b6d0bc8b8735d59dda04a6cbfa0ffddfff9fbdd597b40911d1653171393","target":"record","created_at":"2026-05-18T00:41:37Z","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":"954136c1e96849f220156929f1c42a6af507396a982d6b5563b10c80db43c8a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-11T16:51:47Z","title_canon_sha256":"2232d038cad52a79ff96374da9248d473461d5566cee91bbbbea1b15ffdd930a"},"schema_version":"1.0","source":{"id":"1701.03058","kind":"arxiv","version":2}},"canonical_sha256":"823c7f740ebeef1c662bb195d349e0895680427e1731fe68645749a88499bce2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823c7f740ebeef1c662bb195d349e0895680427e1731fe68645749a88499bce2","first_computed_at":"2026-05-18T00:41:37.586724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:37.586724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tFDP68Um+1d3d0PQE0XxSYVc7UEiyxTHYLOV2nEjc+eCoGvPxyLum4FSB6ZTbsOZ7OouWE8Qw/PQqhFnYGbYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:37.587449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75197b6d0bc8b8735d59dda04a6cbfa0ffddfff9fbdd597b40911d1653171393","sha256:a5a9f63d685952d2dd5345ae6091c5e1c66cd4f04dfec067ef0e69354e6b9e36"],"state_sha256":"29c10bb1cf045df122f11fa4c49a4faac48b525a6d1d1b9a0fc2b1670b592669"}