{"paper":{"title":"Gap-Majority Lemmas in Communication Complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Huacheng Yu, Pachara Sawettamalya","submitted_at":"2026-07-08T13:32:29Z","abstract_excerpt":"We prove an information-theoretically optimal \\emph{gap-majority lemma} in the two-player randomized communication model. For a base function $f: \\mathcal{X} \\to \\{\\pm 1\\}$, its $n$-fold \\emph{gap-majority composition}, denoted $\\mathsf{GapMAJ} \\circ f^n$, takes $n$ inputs $(X_1, \\ldots, X_n)$ and distinguishes whether $f^{+n}(X_1,\\ldots,X_n) := f(X_1) + \\ldots + f(X_n)$ is at least $0.01\\sqrt{n}$ or at most $-0.01\\sqrt{n}$. We show that if computing $f$ with success probability $0.501$ requires $I$ bits of information, then computing $\\mathsf{GapMAJ} \\circ f^n$ with success probability $0.99$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07396","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07396/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"}