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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 $0.99$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.07396","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-08T13:32:29Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"018d071987cc31b06b8198e99675c1b23907696809b5ae17cdf2a2ba7d047868","abstract_canon_sha256":"02a3c16cfeef7c55a77fe0e4311d20d50836200b8f621c17a05984e0f9807ed3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:23.841244Z","signature_b64":"O7DfyZC2sgpy2VegevnaErpVQJxCkrXkukj3gDO8WAt6KFLBpwz8Xwvkes+0WSzvF/yvxQOsLqbk12F3M0oDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e6af70466bc2bfd93602ffd091de12c7e0169f49afb4f135a0eb2c7a3654749","last_reissued_at":"2026-07-09T01:20:23.840795Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:23.840795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $-0.01\\sqrt{n}$. 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