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As an application, we provide several examples of P-recursive sequences of order greater than two."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The sequence possesses a unique dominant root (i.e., one root of the characteristic equation strictly dominates all others in modulus), which is invoked as the structural hypothesis enabling the sufficient positivity condition.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A sufficient condition is derived for ultimate positivity of arbitrary-order P-recursive sequences with a unique dominant root, allowing positivity to be settled by finite initial-term verification, with concrete examples for orders exceeding two.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A sufficient condition proves ultimate positivity for P-recursive sequences of any order with a unique dominant root.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1cc89f4ff7d0f539ae22d7254becc55a4d940e2592a4c723250ae80d8e32b9cd"},"source":{"id":"2605.17013","kind":"arxiv","version":1},"verdict":{"id":"c60e6d4d-a204-4664-9cbe-6d3443ff789a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:00:01.341361Z","strongest_claim":"We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root.","one_line_summary":"A sufficient condition is derived for ultimate positivity of arbitrary-order P-recursive sequences with a unique dominant root, allowing positivity to be settled by finite initial-term verification, with concrete examples for orders exceeding two.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The sequence possesses a unique dominant root (i.e., one root of the characteristic equation strictly dominates all others in modulus), which is invoked as the structural hypothesis enabling the sufficient positivity condition.","pith_extraction_headline":"A sufficient condition proves ultimate positivity for P-recursive sequences of any order with a unique dominant root."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17013/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.015700Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:10:46.972822Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T19:49:48.653083Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T18:51:59.250332Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.188933Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:24.874947Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"75c53d5cd29ecc08cfb4a05f57c5c845d9c12750c544403de14246acf0a53d51"},"references":{"count":18,"sample":[{"doi":"","year":2006,"title":"J.P. 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