{"paper":{"title":"Information Accessibility Limits in Structured NP Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Polynomially many local queries cannot recover sparse violating subsets in near-P-matrix families with constant probability.","cross_cats":["cs.CC","math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Jing-Yuan Wei","submitted_at":"2026-05-01T11:43:51Z","abstract_excerpt":"We study the problem of locating violating principal minors in matrix families lying near the boundary of P-matrices. Rather than viewing this search problem purely through computational complexity, we analyze it from an information-accessibility perspective.\n  We show that, despite strong underlying algebraic structure, the location of a violating subset may remain difficult to infer through local queries. In the sparse-violation regime, local observations typically provide only weak eliminative power, and polynomially many queries accumulate only vanishing mutual information about the hidden"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"any algorithm restricted to polynomially many queries cannot recover the violating subset with constant success probability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The restricted interaction model in which queries provide only local information that does not capture the globally encoded location of the violating subset.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In structured P-matrix families with sparse violations, the violating subset cannot be recovered with constant success probability using polynomially many local queries due to an information-theoretic bottleneck.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Polynomially many local queries cannot recover sparse violating subsets in near-P-matrix families with constant probability.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1640cac97b2a3c158b66e5695dc4b48625833fedfeeea61471a2210e9d8d9796"},"source":{"id":"2605.00953","kind":"arxiv","version":4},"verdict":{"id":"05d1e1f5-13fb-4b24-9b6d-f1522c932ab6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T18:58:21.571308Z","strongest_claim":"any algorithm restricted to polynomially many queries cannot recover the violating subset with constant success probability.","one_line_summary":"In structured P-matrix families with sparse violations, the violating subset cannot be recovered with constant success probability using polynomially many local queries due to an information-theoretic bottleneck.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The restricted interaction model in which queries provide only local information that does not capture the globally encoded location of the violating subset.","pith_extraction_headline":"Polynomially many local queries cannot recover sparse violating subsets in near-P-matrix families with constant probability."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00953/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T19:39:24.686175Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:02:16.192194Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"92fd90e5ed1de5734643a90a90bbb785dc620ee84b6ea2b313c349749f2752de"},"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"}