{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EZIBVQ6XMWHJXYU2BOTBN6R2QF","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":"b75bd91721ddfa9a565a588c9ff18f32484573b6723b48640cef40c29c852aa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-20T19:49:55Z","title_canon_sha256":"575d10bf5d94bfcb0e4c9b8bf0bf58e3c40f2f48340a02719f4f3459d491ff3a"},"schema_version":"1.0","source":{"id":"1408.4783","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4783","created_at":"2026-05-18T01:22:43Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4783v2","created_at":"2026-05-18T01:22:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4783","created_at":"2026-05-18T01:22:43Z"},{"alias_kind":"pith_short_12","alias_value":"EZIBVQ6XMWHJ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EZIBVQ6XMWHJXYU2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EZIBVQ6X","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:82a7335296db447262a1b9e993a8069b84df61b5bcfbae3ac29349560126d157","target":"graph","created_at":"2026-05-18T01:22:43Z","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":"We provide a near-complete classification of the Lorentz spaces $\\Lambda_{\\varphi}$ for which the sequence $\\{S_{n}\\}_{n\\in \\mathbb{N}}$ of partial Fourier sums is almost everywhere convergent along lacunary subsequences. Moreover, under mild assumptions on the fundamental function $\\varphi$, we identify $\\Lambda_{\\varphi}:= L\\log\\log L\\log\\log\\log\\log L$ as the \\emph{largest} Lorentz space on which the lacunary Carleson operator is bounded as a map to $L^{1,\\infty}$. In particular, we disprove a conjecture stated by Konyagin in his 2006 ICM address. Our proof relies on a newly introduced conc","authors_text":"Victor Lie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-20T19:49:55Z","title":"The pointwise convergence of Fourier Series (I). On a conjecture of Konyagin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4783","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:fba80a311e26844c712b894ada93fb6772775547377e4f25271224c50df61bd8","target":"record","created_at":"2026-05-18T01:22:43Z","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":"b75bd91721ddfa9a565a588c9ff18f32484573b6723b48640cef40c29c852aa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-20T19:49:55Z","title_canon_sha256":"575d10bf5d94bfcb0e4c9b8bf0bf58e3c40f2f48340a02719f4f3459d491ff3a"},"schema_version":"1.0","source":{"id":"1408.4783","kind":"arxiv","version":2}},"canonical_sha256":"26501ac3d7658e9be29a0ba616fa3a8169d584f1b828daccffcfdae0687eda44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26501ac3d7658e9be29a0ba616fa3a8169d584f1b828daccffcfdae0687eda44","first_computed_at":"2026-05-18T01:22:43.420176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:43.420176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aSx3MGZPI7SJ+rzQtS2HVDwBh8DtQV47R4sC9YjdBiwkawTkqMXFl8+Id8hTKTk6H6TUlC5E/cNg04YEMxkeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:43.420683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fba80a311e26844c712b894ada93fb6772775547377e4f25271224c50df61bd8","sha256:82a7335296db447262a1b9e993a8069b84df61b5bcfbae3ac29349560126d157"],"state_sha256":"9ce55a20367fccc874ed503e61fc1f8edbe3105515fb5f308ff4ee18960e5a3d"}