{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EQN5E4T4EUDIHL4ATKE4OA3SJB","short_pith_number":"pith:EQN5E4T4","schema_version":"1.0","canonical_sha256":"241bd2727c250683af809a89c70372487c647b73a06ce5c7e117712dfc5dcf46","source":{"kind":"arxiv","id":"1106.0871","version":2},"attestation_state":"computed","paper":{"title":"Estimates for the Square Variation of Partial Sums of Fourier Series and their Rearrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Allison Lewko, Mark Lewko","submitted_at":"2011-06-05T03:44:20Z","abstract_excerpt":"We investigate the square variation operator $V^2$ (which majorizes the partial sum maximal operator) on general orthonormal systems (ONS) of size $N$. We prove that the $L^2$ norm of the $V^2$ operator is bounded by $O(\\ln(N))$ on any ONS. This result is sharp and refines the classical Rademacher-Menshov theorem. We show that this can be improved to $O(\\sqrt{\\ln(N)})$ for the trigonometric system, which is also sharp. We show that for any choice of coefficients, this truncation of the trigonometric system can be rearranged so that the $L^2$ norm of the associated $V^2$ operator is $O(\\sqrt{\\l"},"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":"1106.0871","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-05T03:44:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"45defbb8e811b4086418b8fc47a4dc7037538fcae3d52be720d630f482573032","abstract_canon_sha256":"c38bd95e1fc22f31579c7a8decc4180a3748752f655a8f06c8e92b27d82b08da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:32.336900Z","signature_b64":"RXSfNontX2lOM2CQTeDJ7np8jlzHrXC94+++3Bo/fQDwC0YWjjlMrEl4S9YNDlUZMWC9sm44/+JGMlppWjdwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"241bd2727c250683af809a89c70372487c647b73a06ce5c7e117712dfc5dcf46","last_reissued_at":"2026-05-18T04:03:32.336252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:32.336252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates for the Square Variation of Partial Sums of Fourier Series and their Rearrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Allison Lewko, Mark Lewko","submitted_at":"2011-06-05T03:44:20Z","abstract_excerpt":"We investigate the square variation operator $V^2$ (which majorizes the partial sum maximal operator) on general orthonormal systems (ONS) of size $N$. We prove that the $L^2$ norm of the $V^2$ operator is bounded by $O(\\ln(N))$ on any ONS. This result is sharp and refines the classical Rademacher-Menshov theorem. We show that this can be improved to $O(\\sqrt{\\ln(N)})$ for the trigonometric system, which is also sharp. We show that for any choice of coefficients, this truncation of the trigonometric system can be rearranged so that the $L^2$ norm of the associated $V^2$ operator is $O(\\sqrt{\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0871","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":"1106.0871","created_at":"2026-05-18T04:03:32.336351+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0871v2","created_at":"2026-05-18T04:03:32.336351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0871","created_at":"2026-05-18T04:03:32.336351+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQN5E4T4EUDI","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQN5E4T4EUDIHL4A","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQN5E4T4","created_at":"2026-05-18T12:26:28.662955+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/EQN5E4T4EUDIHL4ATKE4OA3SJB","json":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB.json","graph_json":"https://pith.science/api/pith-number/EQN5E4T4EUDIHL4ATKE4OA3SJB/graph.json","events_json":"https://pith.science/api/pith-number/EQN5E4T4EUDIHL4ATKE4OA3SJB/events.json","paper":"https://pith.science/paper/EQN5E4T4"},"agent_actions":{"view_html":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB","download_json":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB.json","view_paper":"https://pith.science/paper/EQN5E4T4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0871&json=true","fetch_graph":"https://pith.science/api/pith-number/EQN5E4T4EUDIHL4ATKE4OA3SJB/graph.json","fetch_events":"https://pith.science/api/pith-number/EQN5E4T4EUDIHL4ATKE4OA3SJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB/action/storage_attestation","attest_author":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB/action/author_attestation","sign_citation":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB/action/citation_signature","submit_replication":"https://pith.science/pith/EQN5E4T4EUDIHL4ATKE4OA3SJB/action/replication_record"}},"created_at":"2026-05-18T04:03:32.336351+00:00","updated_at":"2026-05-18T04:03:32.336351+00:00"}