{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7NICJ4M7HAVMV7OHB7RKLFHNF2","short_pith_number":"pith:7NICJ4M7","schema_version":"1.0","canonical_sha256":"fb5024f19f382acafdc70fe2a594ed2eb93954c2d07bf18b94c7088de94114b6","source":{"kind":"arxiv","id":"1309.1914","version":4},"attestation_state":"computed","paper":{"title":"Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"cs.CC","authors_text":"James Worrell, Joel Ouaknine","submitted_at":"2013-09-07T22:29:13Z","abstract_excerpt":"We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive. Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is decidable in polynomial space. If we restrict to simple LRS of a fixed order then we obtain a polynomial-time decision procedure. As a complexity lower bound we show that Ultimate Positivity for simple LRS"},"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":"1309.1914","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-09-07T22:29:13Z","cross_cats_sorted":["cs.DM","cs.FL"],"title_canon_sha256":"36dceff81713d7a64de0aca8a43005d64f1aa86dc3ffba3fc7625c9c4ac4d3fa","abstract_canon_sha256":"bef7dc586b0558605cb5c1f61e64fb73305faee193a343cfb7d4c93905083868"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:56.041379Z","signature_b64":"rvUawmyYp2mHEfw9TgCxWr5/61Q710EGWZi2VC63dZk+TfwAZ6YnbLYH1JdzAhj8ZCAbxVABfmyRgEOHCK4fCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb5024f19f382acafdc70fe2a594ed2eb93954c2d07bf18b94c7088de94114b6","last_reissued_at":"2026-05-18T00:46:56.040945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:56.040945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"cs.CC","authors_text":"James Worrell, Joel Ouaknine","submitted_at":"2013-09-07T22:29:13Z","abstract_excerpt":"We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive. Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is decidable in polynomial space. If we restrict to simple LRS of a fixed order then we obtain a polynomial-time decision procedure. As a complexity lower bound we show that Ultimate Positivity for simple LRS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1914","kind":"arxiv","version":4},"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":"1309.1914","created_at":"2026-05-18T00:46:56.041005+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1914v4","created_at":"2026-05-18T00:46:56.041005+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1914","created_at":"2026-05-18T00:46:56.041005+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NICJ4M7HAVM","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NICJ4M7HAVMV7OH","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NICJ4M7","created_at":"2026-05-18T12:27:36.564083+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/7NICJ4M7HAVMV7OHB7RKLFHNF2","json":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2.json","graph_json":"https://pith.science/api/pith-number/7NICJ4M7HAVMV7OHB7RKLFHNF2/graph.json","events_json":"https://pith.science/api/pith-number/7NICJ4M7HAVMV7OHB7RKLFHNF2/events.json","paper":"https://pith.science/paper/7NICJ4M7"},"agent_actions":{"view_html":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2","download_json":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2.json","view_paper":"https://pith.science/paper/7NICJ4M7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1914&json=true","fetch_graph":"https://pith.science/api/pith-number/7NICJ4M7HAVMV7OHB7RKLFHNF2/graph.json","fetch_events":"https://pith.science/api/pith-number/7NICJ4M7HAVMV7OHB7RKLFHNF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2/action/storage_attestation","attest_author":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2/action/author_attestation","sign_citation":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2/action/citation_signature","submit_replication":"https://pith.science/pith/7NICJ4M7HAVMV7OHB7RKLFHNF2/action/replication_record"}},"created_at":"2026-05-18T00:46:56.041005+00:00","updated_at":"2026-05-18T00:46:56.041005+00:00"}