{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:5T3LRJFTG7DGED6JYSLOSGPELB","short_pith_number":"pith:5T3LRJFT","schema_version":"1.0","canonical_sha256":"ecf6b8a4b337c6620fc9c496e919e4585fb4e7ca25a8698e4594159119443f2f","source":{"kind":"arxiv","id":"0909.5158","version":2},"attestation_state":"computed","paper":{"title":"A Three Dimensional Signed Small Ball Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Armen Vagharshakyan, Dmitriy Bilyk, Ioannis Parissis, Michael T. Lacey","submitted_at":"2009-09-28T18:10:23Z","abstract_excerpt":"The Small Ball Inequality is a conjectural lower bound on sums the L-infinity norm of sums of Haar functions supported on dyadic rectangles of a fixed volume in the unit cube. The conjecture is fundamental to questions in discrepancy theory, approximation theory and probability theory. In this article, we concentrate on a special case of the conjecture, and give the best known lower bound in dimension 3, using a conditional expectation argument."},"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":"0909.5158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-09-28T18:10:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"39781b3e20ca3db6058a1b113932be87d380055ba47c9b0ed76f464a7b5a4dc8","abstract_canon_sha256":"8fa5bbbfa9464c5b4c834662b0b760a178b275dee438e7c87dea324d2a6fefda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.272469Z","signature_b64":"KXuYXAFKLytM689oAxPoofZmItiMarHAyP4mJz2dDNDAurK3m2iOqngSX4SD1LfHMA88xE/nyXUYHDw/UcKaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf6b8a4b337c6620fc9c496e919e4585fb4e7ca25a8698e4594159119443f2f","last_reissued_at":"2026-05-18T03:56:34.271744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.271744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Three Dimensional Signed Small Ball Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Armen Vagharshakyan, Dmitriy Bilyk, Ioannis Parissis, Michael T. Lacey","submitted_at":"2009-09-28T18:10:23Z","abstract_excerpt":"The Small Ball Inequality is a conjectural lower bound on sums the L-infinity norm of sums of Haar functions supported on dyadic rectangles of a fixed volume in the unit cube. The conjecture is fundamental to questions in discrepancy theory, approximation theory and probability theory. In this article, we concentrate on a special case of the conjecture, and give the best known lower bound in dimension 3, using a conditional expectation argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5158","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0909.5158","created_at":"2026-05-18T03:56:34.271854+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.5158v2","created_at":"2026-05-18T03:56:34.271854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5158","created_at":"2026-05-18T03:56:34.271854+00:00"},{"alias_kind":"pith_short_12","alias_value":"5T3LRJFTG7DG","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"5T3LRJFTG7DGED6J","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"5T3LRJFT","created_at":"2026-05-18T12:25:58.837520+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/5T3LRJFTG7DGED6JYSLOSGPELB","json":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB.json","graph_json":"https://pith.science/api/pith-number/5T3LRJFTG7DGED6JYSLOSGPELB/graph.json","events_json":"https://pith.science/api/pith-number/5T3LRJFTG7DGED6JYSLOSGPELB/events.json","paper":"https://pith.science/paper/5T3LRJFT"},"agent_actions":{"view_html":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB","download_json":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB.json","view_paper":"https://pith.science/paper/5T3LRJFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.5158&json=true","fetch_graph":"https://pith.science/api/pith-number/5T3LRJFTG7DGED6JYSLOSGPELB/graph.json","fetch_events":"https://pith.science/api/pith-number/5T3LRJFTG7DGED6JYSLOSGPELB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB/action/storage_attestation","attest_author":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB/action/author_attestation","sign_citation":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB/action/citation_signature","submit_replication":"https://pith.science/pith/5T3LRJFTG7DGED6JYSLOSGPELB/action/replication_record"}},"created_at":"2026-05-18T03:56:34.271854+00:00","updated_at":"2026-05-18T03:56:34.271854+00:00"}