{"paper":{"title":"Problem of Finding an Optimal Piecewise Linear Path Connecting Two Given Points with the Possibility of Making n Turns","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Under some condition all interior vertices of an admissible n-turn path between two points lie in a specific region, and every admissible sequence of corner points admits an explicit description.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Nefedov V.N","submitted_at":"2026-05-14T22:19:03Z","abstract_excerpt":"We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed bound). Under some condition, we characterize the region to which all interior vertices of such a path must belong (Theorem 1). It is shown that for any point from this region, there exists a polygonal line satisfying the given constraints (Lemma 1). Based on these findings, an explicit expression is derived (Theorem 2) that describes the collection of all admiss"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under some condition, all interior vertices of an admissible n-turn polygonal line belong to a specific region (Theorem 1); an explicit expression describes the collection of all admissible sequences of corner points (Theorem 2), which is then approximated by a finite family for optimization algorithms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The unspecified 'some condition' under which the region characterization in Theorem 1 holds; without knowing or verifying this condition the claimed region and subsequent sequence expression may not apply to the general case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Characterizes admissible regions and sequences for bounded-turn n-segment paths and builds finite approximations for optimization algorithms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Under some condition all interior vertices of an admissible n-turn path between two points lie in a specific region, and every admissible sequence of corner points admits an explicit description.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"72ab88f7d6758cd64e95f410dbfbb30fabbb34b6f2579a7b0d1538d6fb833ea1"},"source":{"id":"2605.15449","kind":"arxiv","version":1},"verdict":{"id":"fbab1034-7a83-4fef-91ee-0eb2d723fef1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T14:28:53.803238Z","strongest_claim":"Under some condition, all interior vertices of an admissible n-turn polygonal line belong to a specific region (Theorem 1); an explicit expression describes the collection of all admissible sequences of corner points (Theorem 2), which is then approximated by a finite family for optimization algorithms.","one_line_summary":"Characterizes admissible regions and sequences for bounded-turn n-segment paths and builds finite approximations for optimization algorithms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The unspecified 'some condition' under which the region characterization in Theorem 1 holds; without knowing or verifying this condition the claimed region and subsequent sequence expression may not apply to the general case.","pith_extraction_headline":"Under some condition all interior vertices of an admissible n-turn path between two points lie in a specific region, and every admissible sequence of corner points admits an explicit description."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15449/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T15:51:56.241280Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T15:50:05.014142Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T15:01:17.619014Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:37:53.784045Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.111784Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.679079Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8387b51787707c67299733f625fa021c1c5e92e388d2427aad87f392f325fcde"},"references":{"count":8,"sample":[{"doi":"","year":2025,"title":"Methods of Approximation of Two Dimensional Sets by Finite Sets and Their Application to Some Geometric Optimization 99 Problems","work_id":"82c34db7-95b7-460e-ac6c-d9fe5e3e3b2f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Problem of Finding an Optimal Piecewise Linear Route with n Turns","work_id":"d947a47a-6376-4a44-95e4-95c2180fe03e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Dynamic Programming","work_id":"223006b2-9e82-46ac-8374-d6abedfcc670","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Cormen, Thomas H., Charles E. 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