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It is the largest size of a $\\mathsf{CSP}$ instance admitting no smaller subinstance with the same satisfying assignments.\n  We study non-redundancy $\\mathsf{NRD}_n(R)$ for Boolean symmetric $\\mathsf{CSPs}$ defined by an $r$-ary relation $R$ whose value depends only on Hamming weight. An instance of $\\mathsf{CSP}(R)$ has $n$ variables and c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result is a near-complete classification of the asymptotic growth of NRD_n(R) for symmetric Boolean predicates of arity at most 5. We resolve every predicate of arity at most 4 and all but two predicates of arity 5.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The computational experiments are assumed to have exhaustively enumerated and correctly classified all symmetric Boolean relations of arity at most 4 and all but two of arity 5; the algebraic criteria for t-balancedness are assumed to be tight for the unresolved cases.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symmetric Boolean CSPs of arity at most 5 have their non-redundancy growth rates classified as O(n), O(n^2), or O(n^3), with all arity-4 cases and most arity-5 cases resolved.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7e3a578c01d85ba6e1b54d44735c117b4c4889f4325a0b5be715000449af3e85"},"source":{"id":"2605.14007","kind":"arxiv","version":1},"verdict":{"id":"54f31192-e114-4be3-9373-9a4397d2f708","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:49:10.628545Z","strongest_claim":"Our main result is a near-complete classification of the asymptotic growth of NRD_n(R) for symmetric Boolean predicates of arity at most 5. 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