{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SYQRKES3MB47NFW3OV6IEBKIP7","short_pith_number":"pith:SYQRKES3","schema_version":"1.0","canonical_sha256":"962115125b6079f696db757c8205487fe4780d747891de8b5249ae1cdb2f4d88","source":{"kind":"arxiv","id":"1301.4870","version":2},"attestation_state":"computed","paper":{"title":"From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Kurt Mehlhorn, Michael Sagraloff, Pengming Wang","submitted_at":"2013-01-21T14:14:07Z","abstract_excerpt":"We present an algorithm for isolating the roots of an arbitrary complex polynomial $p$ that also works for polynomials with multiple roots provided that the number $k$ of distinct roots is given as part of the input. It outputs $k$ pairwise disjoint disks each containing one of the distinct roots of $p$, and its multiplicity. The algorithm uses approximate factorization as a subroutine.\n  In addition, we apply the new root isolation algorithm to a recent algorithm for computing the topology of a real planar algebraic curve specified as the zero set of a bivariate integer polynomial and for iso"},"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":"1301.4870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-21T14:14:07Z","cross_cats_sorted":[],"title_canon_sha256":"a6059bb076183d794b03a7abfee64bb8c4c075fdb43c0d238bc29b031d0eaa3a","abstract_canon_sha256":"7f7057c9a87cbb51f90e43e8e97e2f2ccd86af49d2ed55a85efef7f11a04cbb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:24.443281Z","signature_b64":"0PVt22bH6k+RJXVo7H3AEr9fGAIOPXBsa1g2e2mKg5WhIVUmke8YllExYy7kCbFzL/6NfKeBvREbzl2LCw3HCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"962115125b6079f696db757c8205487fe4780d747891de8b5249ae1cdb2f4d88","last_reissued_at":"2026-05-18T03:01:24.442641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:24.442641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Kurt Mehlhorn, Michael Sagraloff, Pengming Wang","submitted_at":"2013-01-21T14:14:07Z","abstract_excerpt":"We present an algorithm for isolating the roots of an arbitrary complex polynomial $p$ that also works for polynomials with multiple roots provided that the number $k$ of distinct roots is given as part of the input. It outputs $k$ pairwise disjoint disks each containing one of the distinct roots of $p$, and its multiplicity. The algorithm uses approximate factorization as a subroutine.\n  In addition, we apply the new root isolation algorithm to a recent algorithm for computing the topology of a real planar algebraic curve specified as the zero set of a bivariate integer polynomial and for iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4870","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":"1301.4870","created_at":"2026-05-18T03:01:24.442733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4870v2","created_at":"2026-05-18T03:01:24.442733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4870","created_at":"2026-05-18T03:01:24.442733+00:00"},{"alias_kind":"pith_short_12","alias_value":"SYQRKES3MB47","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SYQRKES3MB47NFW3","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SYQRKES3","created_at":"2026-05-18T12:27:59.945178+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/SYQRKES3MB47NFW3OV6IEBKIP7","json":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7.json","graph_json":"https://pith.science/api/pith-number/SYQRKES3MB47NFW3OV6IEBKIP7/graph.json","events_json":"https://pith.science/api/pith-number/SYQRKES3MB47NFW3OV6IEBKIP7/events.json","paper":"https://pith.science/paper/SYQRKES3"},"agent_actions":{"view_html":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7","download_json":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7.json","view_paper":"https://pith.science/paper/SYQRKES3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4870&json=true","fetch_graph":"https://pith.science/api/pith-number/SYQRKES3MB47NFW3OV6IEBKIP7/graph.json","fetch_events":"https://pith.science/api/pith-number/SYQRKES3MB47NFW3OV6IEBKIP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7/action/storage_attestation","attest_author":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7/action/author_attestation","sign_citation":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7/action/citation_signature","submit_replication":"https://pith.science/pith/SYQRKES3MB47NFW3OV6IEBKIP7/action/replication_record"}},"created_at":"2026-05-18T03:01:24.442733+00:00","updated_at":"2026-05-18T03:01:24.442733+00:00"}