{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4DRU6LTE3B33VHFQU7CV6NC553","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":"f10a148ba3fbdcc0ad44bcc805053ae68242e1acd4919907c9ff2f601baa54fc","cross_cats_sorted":["cs.MS","cs.NA","math.AG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-01-23T13:38:46Z","title_canon_sha256":"6bff3a32f192af59657e20ec5b0888360a6c5c38838f0f9f85bf350a3cb9b54b"},"schema_version":"1.0","source":{"id":"1101.4369","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4369","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4369v2","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4369","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"4DRU6LTE3B33","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4DRU6LTE3B33VHFQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4DRU6LTE","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:1a03a26cdff0f2730494f629f23451c20e06b0f20f3776f075cd2672a2b24d1d","target":"graph","created_at":"2026-05-18T04:22:39Z","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":"We present algorithmic, complexity and implementation results for the problem of isolating the real roots of a univariate polynomial in $B_{\\alpha} \\in L[y]$, where $L=\\QQ(\\alpha)$ is a simple algebraic extension of the rational numbers. We consider two approaches for tackling the problem. In the first approach using resultant computations we perform a reduction to a polynomial with integer coefficients. We compute separation bounds for the roots, and using them we deduce that we can isolate the real roots of $B_{\\alpha}$ in $\\sOB(N^{10})$, where $N$ is an upper bound on all the quantities (de","authors_text":"Adam Strzebonski, Elias Tsigaridas","cross_cats":["cs.MS","cs.NA","math.AG","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-01-23T13:38:46Z","title":"Univariate real root isolation in an extension field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4369","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":"sha256:04607883b97fd011bf546a6086d388d0023be810740088e49700e2478a59b9e2","target":"record","created_at":"2026-05-18T04:22:39Z","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":"f10a148ba3fbdcc0ad44bcc805053ae68242e1acd4919907c9ff2f601baa54fc","cross_cats_sorted":["cs.MS","cs.NA","math.AG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-01-23T13:38:46Z","title_canon_sha256":"6bff3a32f192af59657e20ec5b0888360a6c5c38838f0f9f85bf350a3cb9b54b"},"schema_version":"1.0","source":{"id":"1101.4369","kind":"arxiv","version":2}},"canonical_sha256":"e0e34f2e64d877ba9cb0a7c55f345deefb1d2aeee20b52853d04f96b32bd4c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0e34f2e64d877ba9cb0a7c55f345deefb1d2aeee20b52853d04f96b32bd4c02","first_computed_at":"2026-05-18T04:22:39.887707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:39.887707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Evstz/PD32Up7h2LfEjVm73zlPaZG9EX/BKfD5lVfch1IIpH5+1/FgRDgTMCm9HHG2glqyouiB69vmxpbtkbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:39.888099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4369","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04607883b97fd011bf546a6086d388d0023be810740088e49700e2478a59b9e2","sha256:1a03a26cdff0f2730494f629f23451c20e06b0f20f3776f075cd2672a2b24d1d"],"state_sha256":"91496528aa63f4d6647fe234a12210a34b03bbe83bc6fc04931493eac6c70b02"}