{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PBAMWZJKIYF25WXCDJKBBYI7VB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9c6a90fda77092334a6d1eced88ab5eb37e585b1400bcacfd2bfb5b0aefc35d4","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-17T00:06:02Z","title_canon_sha256":"355c6c0c375aefc10073f49e167a361d59343b9d62bcc26355f11df19b9db3ec"},"schema_version":"1.0","source":{"id":"2404.10961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.10961","created_at":"2026-07-05T08:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"2404.10961v2","created_at":"2026-07-05T08:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.10961","created_at":"2026-07-05T08:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"PBAMWZJKIYF2","created_at":"2026-07-05T08:43:28Z"},{"alias_kind":"pith_short_16","alias_value":"PBAMWZJKIYF25WXC","created_at":"2026-07-05T08:43:28Z"},{"alias_kind":"pith_short_8","alias_value":"PBAMWZJK","created_at":"2026-07-05T08:43:28Z"}],"graph_snapshots":[{"event_id":"sha256:99749b43edc13d40da7499fa3e1a91c328d4921b09d6c7bbffc69e0ffee7f300","target":"graph","created_at":"2026-07-05T08:43:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.10961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). Let $X$ be a $k$-dimensional HDX. 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","authors_text":"Max Hopkins, Yotam Dikstein","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-17T00:06:02Z","title":"Chernoff Bounds and Reverse Hypercontractivity on HDX"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.10961","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:daa16d32a2fa653e1016f8f1c6986ccc426ba504038c6980af2f466fc88f5b9c","target":"record","created_at":"2026-07-05T08:43:28Z","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":"9c6a90fda77092334a6d1eced88ab5eb37e585b1400bcacfd2bfb5b0aefc35d4","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-17T00:06:02Z","title_canon_sha256":"355c6c0c375aefc10073f49e167a361d59343b9d62bcc26355f11df19b9db3ec"},"schema_version":"1.0","source":{"id":"2404.10961","kind":"arxiv","version":2}},"canonical_sha256":"7840cb652a460baedae21a5410e11fa87ff2eb66638197ac4f01bc05fa033674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7840cb652a460baedae21a5410e11fa87ff2eb66638197ac4f01bc05fa033674","first_computed_at":"2026-07-05T08:43:28.003020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:43:28.003020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mrlhU1ccXomsyePUwFOckqzYjg+BD3wlHGGa8Z8CYy+swNHn9Quphbmjhx10Io5HwsxeqWiXthMM7aRPiTN7Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:43:28.003459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.10961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daa16d32a2fa653e1016f8f1c6986ccc426ba504038c6980af2f466fc88f5b9c","sha256:99749b43edc13d40da7499fa3e1a91c328d4921b09d6c7bbffc69e0ffee7f300"],"state_sha256":"654c2bde83a135d9d060e0f1ca7f32cfa871b3b6f961f044086f2d198cb5a884"}