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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","authors_text":"Jing-Yuan Wei","cross_cats":["cs.CC","math.IT","math.OC"],"headline":"Polynomially many local queries cannot recover sparse violating subsets in near-P-matrix families with constant probability.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-05-01T11:43:51Z","title":"Information Accessibility Limits in Structured NP Search"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.00953","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-09T18:58:21.571308Z","id":"05d1e1f5-13fb-4b24-9b6d-f1522c932ab6","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Polynomially many local queries cannot recover sparse violating subsets in near-P-matrix families with constant probability.","strongest_claim":"any algorithm restricted to polynomially many queries cannot recover the violating subset with constant success probability.","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."}},"verdict_id":"05d1e1f5-13fb-4b24-9b6d-f1522c932ab6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b91c38db5474ead6fb3f30216785a586058f0c2035db5c91e270e562b945fbf8","target":"record","created_at":"2026-05-22T01:04:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"83596933bb8a40c4b4a72176504100a802e5e61c8bbd0b72dc63ad6aac9d6f7e","cross_cats_sorted":["cs.CC","math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-05-01T11:43:51Z","title_canon_sha256":"423140d92fcc5c9c998f826dbce7c8039908fa1bf60c996ef05b242f9ffad90c"},"schema_version":"1.0","source":{"id":"2605.00953","kind":"arxiv","version":4}},"canonical_sha256":"e521b29e847fe5f05a65ea0869cd93c79a452821e47c7328ce80347611c56a18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e521b29e847fe5f05a65ea0869cd93c79a452821e47c7328ce80347611c56a18","first_computed_at":"2026-05-22T01:04:04.002007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:04.002007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ksHuUghgPeQzj5GbBOXyW6StxJ7/uhu05BsNUybUy8Xm+2bOkoVirpwEaOUff16Kyoy2Dpy078VrWo2qvA8zBg==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:04.002865Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.00953","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b91c38db5474ead6fb3f30216785a586058f0c2035db5c91e270e562b945fbf8","sha256:2f2644dfa6d21c3e406576a7dbb6c3b21837399fc90aa65519eb63352282f26d"],"state_sha256":"b3809f249f2afb6f3330d6b83214e849b194d38d71a99d61be667348b9e922ac"}