{"paper":{"title":"Implementation of Polynomial NP-Complete Algorithms Based on the NP Verifier Simulation Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Fully specified deterministic Turing machines solve SAT and Subset-Sum in polynomial time via an improved verifier simulation framework.","cross_cats":["cs.FL"],"primary_cat":"cs.CC","authors_text":"Changryeol Lee (Independent Researcher)","submitted_at":"2026-02-11T16:17:36Z","abstract_excerpt":"While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive.\n  In this paper, we construct fully specified deterministic certificate-oblivious verifier Turing machines for SAT and Subset-Sum within an improved NP verifier simulation framework. A key contribution of this work is the development of a functional implementation that bridges the gap between theoretical proofs and executable software. Our improved feasible-graph construction yields a theoretical reduction in the asymptotic pol"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct fully specified deterministic Turing Machines (DTMs) for SAT and Subset-Sum within an improved NP verifier simulation framework. The complete Python implementation behaves in accordance with the predicted polynomial-time bounds.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the improved feasible-graph construction and edge-extension mechanisms convert the nondeterministic verifier simulation into a deterministic polynomial-time procedure without introducing hidden exponential factors in the worst case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Authors supply deterministic polynomial-time Turing machines and Python code for the NP-complete problems SAT and Subset-Sum via an enhanced NP verifier simulation framework.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fully specified deterministic Turing machines solve SAT and Subset-Sum in polynomial time via an improved verifier simulation framework.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9d90e31faf72c0cf9deb0568249f9c809b85d5d3b946f6d3d7f841d817c7319f"},"source":{"id":"2602.10991","kind":"arxiv","version":4},"verdict":{"id":"63a00b2a-b5bb-4fde-bab3-ad3da7b56f39","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T05:41:28.825613Z","strongest_claim":"We construct fully specified deterministic Turing Machines (DTMs) for SAT and Subset-Sum within an improved NP verifier simulation framework. The complete Python implementation behaves in accordance with the predicted polynomial-time bounds.","one_line_summary":"Authors supply deterministic polynomial-time Turing machines and Python code for the NP-complete problems SAT and Subset-Sum via an enhanced NP verifier simulation framework.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the improved feasible-graph construction and edge-extension mechanisms convert the nondeterministic verifier simulation into a deterministic polynomial-time procedure without introducing hidden exponential factors in the worst case.","pith_extraction_headline":"Fully specified deterministic Turing machines solve SAT and Subset-Sum in polynomial time via an improved verifier simulation framework."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.10991/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}