{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W377DYZWKRMNUPWXIRMTLUBGVY","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":"fb331d4473dd10c09610f2f5127f06bda9f1de0ed37b26b13b807b270d681d03","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:58:24Z","title_canon_sha256":"b78be4b6b0acebde31c52ba009c94e8e5013601a14091fa2c09ae3ae50ddb025"},"schema_version":"1.0","source":{"id":"2606.30411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30411","created_at":"2026-06-30T02:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30411v1","created_at":"2026-06-30T02:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30411","created_at":"2026-06-30T02:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"W377DYZWKRMN","created_at":"2026-06-30T02:18:14Z"},{"alias_kind":"pith_short_16","alias_value":"W377DYZWKRMNUPWX","created_at":"2026-06-30T02:18:14Z"},{"alias_kind":"pith_short_8","alias_value":"W377DYZW","created_at":"2026-06-30T02:18:14Z"}],"graph_snapshots":[{"event_id":"sha256:ca3a0c06ffddc1491e9d547c4e2c5f4d1efd05c94b4b88da8bd984bee48e376c","target":"graph","created_at":"2026-06-30T02:18:14Z","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/2606.30411/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\epsilon_{ij}, i,j\\geq 1$ be independent Rademacher variables. We prove \\begin{equation*} \\mathbb{E} \\max_{1\\leq j\\leq p}\\left|\\frac{1}{n}\\sum_{i=1}^n\\epsilon_{ij}\\right| \\geq \\min\\left\\{\\frac{255}{256},\\frac{1}{\\sqrt{2\\log 2}}\\sqrt{\\frac{\\log(2p)}{n}}\\right\\}. \\end{equation*} The equality is attained, for instance, by $(n,p)=(2,1)$ and $(n,p)=(2,8).$ We also discuss the optimality of the numerical constants.","authors_text":"Woonyoung Chang","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:58:24Z","title":"Notes on constants for maxima of Rademacher averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30411","kind":"arxiv","version":1},"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:d9cbd750e33396439053146767c8779bcd94144f48abcbc0af23b6c9ee83c572","target":"record","created_at":"2026-06-30T02:18:14Z","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":"fb331d4473dd10c09610f2f5127f06bda9f1de0ed37b26b13b807b270d681d03","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:58:24Z","title_canon_sha256":"b78be4b6b0acebde31c52ba009c94e8e5013601a14091fa2c09ae3ae50ddb025"},"schema_version":"1.0","source":{"id":"2606.30411","kind":"arxiv","version":1}},"canonical_sha256":"b6fff1e3365458da3ed7445935d026ae36794d7814e636219e97d7e22fe7266e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6fff1e3365458da3ed7445935d026ae36794d7814e636219e97d7e22fe7266e","first_computed_at":"2026-06-30T02:18:14.250055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:14.250055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2tMf+aN3rmbJcplBVHsjfjLGn1pFkS+4YBsbOmWtY2sAD/vDaBF6hyDjPxlQK3ukf3C1yP22Gkw4KWpM7j4OCw==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:14.250513Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9cbd750e33396439053146767c8779bcd94144f48abcbc0af23b6c9ee83c572","sha256:ca3a0c06ffddc1491e9d547c4e2c5f4d1efd05c94b4b88da8bd984bee48e376c"],"state_sha256":"6d7f80d6e98c5c976e37ddd47ffd96c9d46897006d2d2fd4dc390004da27b371"}