{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VVLDXVCY5TT4WKRHPGCBFFHJWD","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":"ffbaaf4ff1c3e659509daa5b2e485ad7cf9ddf0cf18a2442ab14ddf43dd67562","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-08T01:16:37Z","title_canon_sha256":"cec4c40ab544c161d3d147619a2cee66f1064716de29ae9dcebab617d854ab6d"},"schema_version":"1.0","source":{"id":"1112.1744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1744","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1744v2","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1744","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"VVLDXVCY5TT4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VVLDXVCY5TT4WKRH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VVLDXVCY","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e0809e6f3d1bf92eebb92b77aabeda2439239edae80f3f0eb3a9ce98e87189ef","target":"graph","created_at":"2026-05-18T04:02:26Z","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"},"paper":{"abstract_excerpt":"For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the\n  Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result of Hunt-Young and is a weighted extension of a variation norm Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses phase plane analysis and a weighted extension of a variational inequality of Lepingle.","authors_text":"Michael T. Lacey, Yen Do","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-08T01:16:37Z","title":"Weighted bounds for variational Walsh-Fourier series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1744","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":"sha256:7025af3bec59a706f79b2d0b68e838b3c27516a2f53e8438a5ec2505c5f79763","target":"record","created_at":"2026-05-18T04:02:26Z","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":"ffbaaf4ff1c3e659509daa5b2e485ad7cf9ddf0cf18a2442ab14ddf43dd67562","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-08T01:16:37Z","title_canon_sha256":"cec4c40ab544c161d3d147619a2cee66f1064716de29ae9dcebab617d854ab6d"},"schema_version":"1.0","source":{"id":"1112.1744","kind":"arxiv","version":2}},"canonical_sha256":"ad563bd458ece7cb2a2779841294e9b0cb506dbf3cee61eb5e651463725c2f77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad563bd458ece7cb2a2779841294e9b0cb506dbf3cee61eb5e651463725c2f77","first_computed_at":"2026-05-18T04:02:26.869785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.869785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KcMxZXOO4NHH/8rGVjXVgNYENotrsiECTi2dtjMAof27MoHBeImfIMTbpj5RWixFfP6zoswH+7aJlVMYVhfKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.870247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7025af3bec59a706f79b2d0b68e838b3c27516a2f53e8438a5ec2505c5f79763","sha256:e0809e6f3d1bf92eebb92b77aabeda2439239edae80f3f0eb3a9ce98e87189ef"],"state_sha256":"3950dc4d7c8d1395403b67272ac08e3bdec9b3defaa5450def556398e42b04ff"}