{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JG5TUD2J4Q4AO7AEG5237UKSTP","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":"ae4410d6903d40e60af131e9bf1fa6aba762501fce655783b278f7be4442e038","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-01T22:29:14Z","title_canon_sha256":"48dce0e57d01d88859800245a55a9a9b0f314ce9c6160b47aa36348071df72ac"},"schema_version":"1.0","source":{"id":"1705.00729","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00729","created_at":"2026-05-29T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00729v3","created_at":"2026-05-29T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00729","created_at":"2026-05-29T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"JG5TUD2J4Q4A","created_at":"2026-05-29T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"JG5TUD2J4Q4AO7AE","created_at":"2026-05-29T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"JG5TUD2J","created_at":"2026-05-29T01:04:49Z"}],"graph_snapshots":[{"event_id":"sha256:519dacbd8f3971cbb6db3d801367f99a4eaba9cfc82425493bc31a53f086935f","target":"graph","created_at":"2026-05-29T01:04:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.00729/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black box polynomial, represented by an oracle (black box subroutine) for its evaluation rather than in monomial basis - by coefficients. We propose further empirical acceleration, for which we combine these iterations with Ehrlich's (aka Aberth's), Newton's, or Schroeder's. Our combinations of Ehrlich/Newton/Schroeder's and subdivision iterations can be applied to","authors_text":"Victor Y. Pan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-01T22:29:14Z","title":"New Combinations of Polynomial Root-Finding Iterations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00729","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:a229d3a8ba179a1f45f4a3bb6eac31fdd7952b16f95644fdfbdb6042710e7106","target":"record","created_at":"2026-05-29T01:04:49Z","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":"ae4410d6903d40e60af131e9bf1fa6aba762501fce655783b278f7be4442e038","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-01T22:29:14Z","title_canon_sha256":"48dce0e57d01d88859800245a55a9a9b0f314ce9c6160b47aa36348071df72ac"},"schema_version":"1.0","source":{"id":"1705.00729","kind":"arxiv","version":3}},"canonical_sha256":"49bb3a0f49e438077c043775bfd1529bd791d751d7f6a0311ee91ce7097c420e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49bb3a0f49e438077c043775bfd1529bd791d751d7f6a0311ee91ce7097c420e","first_computed_at":"2026-05-29T01:04:49.225683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:49.225683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ExJTyvPstnN2nJ9Zhyss7xtmfEysV8dahqGFP3AmytQ10v2X4eWHXlbIxYvliHR/sJL3H7m0KbPF/kf2tUmhBw==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:49.226332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00729","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a229d3a8ba179a1f45f4a3bb6eac31fdd7952b16f95644fdfbdb6042710e7106","sha256:519dacbd8f3971cbb6db3d801367f99a4eaba9cfc82425493bc31a53f086935f"],"state_sha256":"334a97a06ed0b1c25a953e241ccf34f9448bfb0549dfc8f84ac45e6e62dc1a11"}