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We show for any $i\\leq k$ and $f:X(i)\\to [0,1]$: \\[\\Pr_{s\\in X(k)}\\left[\\left|\\underset{{t\\subseteq s}}{\\mathbb{E}}[f(t)]-\\mu\\right|\\geq\\varepsilon\\right]\\leq exp\\left(-\\varepsilon^2\\frac{k}{i}\\right).\\] Using this fact, we prove that high dimensional expanders are reverse hypercontractive, a powerful functional inequality from discrete analysis implying that for any sets $A,B \\subset X(k)$, the probability a $\\rho$-correlated pair passes between them is at leas"},"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":"2404.10961","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-17T00:06:02Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"355c6c0c375aefc10073f49e167a361d59343b9d62bcc26355f11df19b9db3ec","abstract_canon_sha256":"9c6a90fda77092334a6d1eced88ab5eb37e585b1400bcacfd2bfb5b0aefc35d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:43:28.003459Z","signature_b64":"mrlhU1ccXomsyePUwFOckqzYjg+BD3wlHGGa8Z8CYy+swNHn9Quphbmjhx10Io5HwsxeqWiXthMM7aRPiTN7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7840cb652a460baedae21a5410e11fa87ff2eb66638197ac4f01bc05fa033674","last_reissued_at":"2026-07-05T08:43:28.003020Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:43:28.003020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chernoff Bounds and Reverse Hypercontractivity on HDX","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Max Hopkins, Yotam Dikstein","submitted_at":"2024-04-17T00:06:02Z","abstract_excerpt":"We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). 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