{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:W377DYZWKRMNUPWXIRMTLUBGVY","short_pith_number":"pith:W377DYZW","schema_version":"1.0","canonical_sha256":"b6fff1e3365458da3ed7445935d026ae36794d7814e636219e97d7e22fe7266e","source":{"kind":"arxiv","id":"2606.30411","version":1},"attestation_state":"computed","paper":{"title":"Notes on constants for maxima of Rademacher averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Woonyoung Chang","submitted_at":"2026-06-29T14:58:24Z","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."},"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":"2606.30411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:58:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"b78be4b6b0acebde31c52ba009c94e8e5013601a14091fa2c09ae3ae50ddb025","abstract_canon_sha256":"fb331d4473dd10c09610f2f5127f06bda9f1de0ed37b26b13b807b270d681d03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:14.250513Z","signature_b64":"2tMf+aN3rmbJcplBVHsjfjLGn1pFkS+4YBsbOmWtY2sAD/vDaBF6hyDjPxlQK3ukf3C1yP22Gkw4KWpM7j4OCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6fff1e3365458da3ed7445935d026ae36794d7814e636219e97d7e22fe7266e","last_reissued_at":"2026-06-30T02:18:14.250055Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:14.250055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on constants for maxima of Rademacher averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Woonyoung Chang","submitted_at":"2026-06-29T14:58:24Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30411","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/2606.30411/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.30411","created_at":"2026-06-30T02:18:14.250116+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30411v1","created_at":"2026-06-30T02:18:14.250116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30411","created_at":"2026-06-30T02:18:14.250116+00:00"},{"alias_kind":"pith_short_12","alias_value":"W377DYZWKRMN","created_at":"2026-06-30T02:18:14.250116+00:00"},{"alias_kind":"pith_short_16","alias_value":"W377DYZWKRMNUPWX","created_at":"2026-06-30T02:18:14.250116+00:00"},{"alias_kind":"pith_short_8","alias_value":"W377DYZW","created_at":"2026-06-30T02:18:14.250116+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY","json":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY.json","graph_json":"https://pith.science/api/pith-number/W377DYZWKRMNUPWXIRMTLUBGVY/graph.json","events_json":"https://pith.science/api/pith-number/W377DYZWKRMNUPWXIRMTLUBGVY/events.json","paper":"https://pith.science/paper/W377DYZW"},"agent_actions":{"view_html":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY","download_json":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY.json","view_paper":"https://pith.science/paper/W377DYZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30411&json=true","fetch_graph":"https://pith.science/api/pith-number/W377DYZWKRMNUPWXIRMTLUBGVY/graph.json","fetch_events":"https://pith.science/api/pith-number/W377DYZWKRMNUPWXIRMTLUBGVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY/action/storage_attestation","attest_author":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY/action/author_attestation","sign_citation":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY/action/citation_signature","submit_replication":"https://pith.science/pith/W377DYZWKRMNUPWXIRMTLUBGVY/action/replication_record"}},"created_at":"2026-06-30T02:18:14.250116+00:00","updated_at":"2026-06-30T02:18:14.250116+00:00"}