{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VC75OIZHYHGLTS4OD455RUURX7","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":"a60cf7a7b49bc92ba8ef90efb74dca5b78c6abf8a6cb667dcb4a1dd3ff1116e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-25T12:07:56Z","title_canon_sha256":"b4d71993aedf0825952df0e6a031b052b8ef4383fb260134fed6bff8bc67a24c"},"schema_version":"1.0","source":{"id":"1110.5478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5478","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5478v1","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5478","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"VC75OIZHYHGL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VC75OIZHYHGLTS4O","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VC75OIZH","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:8b92eafaf2bd2388137224f3559846d3528c1580777d1c39f49d4b9dcfacb58c","target":"graph","created_at":"2026-05-18T04:10:22Z","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 study the size, in terms of the Hausdorff dimension, of the subsets of $\\mathbb T$ such that the Fourier series of a generic function in $L^1(\\TT)$, $L^p(\\TT)$ or in $\\mathcal C(\\mathbb T)$ may behave badly. Genericity is related to the Baire category theorem or to the notion of prevalence.","authors_text":"Fr\\'ed\\'eric Bayart, Yanick Heurteaux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-25T12:07:56Z","title":"Multifractal analysis of the divergence of Fourier series: the extreme cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5478","kind":"arxiv","version":1},"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":"sha256:56db01998efad204c4ef854151e3dc560db31a6b75a9e092375aa13366c62047","target":"record","created_at":"2026-05-18T04:10:22Z","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":"a60cf7a7b49bc92ba8ef90efb74dca5b78c6abf8a6cb667dcb4a1dd3ff1116e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-25T12:07:56Z","title_canon_sha256":"b4d71993aedf0825952df0e6a031b052b8ef4383fb260134fed6bff8bc67a24c"},"schema_version":"1.0","source":{"id":"1110.5478","kind":"arxiv","version":1}},"canonical_sha256":"a8bfd72327c1ccb9cb8e1f3bd8d291bfc616cbc3c80d98ef1d8dc4d6213e383e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8bfd72327c1ccb9cb8e1f3bd8d291bfc616cbc3c80d98ef1d8dc4d6213e383e","first_computed_at":"2026-05-18T04:10:22.829176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:22.829176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XYoJMh87mUQymRKL3QAFM4kAn1gkv+BYjv1dEZuOioA7ADy26fdO3mhozHPrI7i0Isn8EzQ9w5ydmmhvZVfFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:22.829583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56db01998efad204c4ef854151e3dc560db31a6b75a9e092375aa13366c62047","sha256:8b92eafaf2bd2388137224f3559846d3528c1580777d1c39f49d4b9dcfacb58c"],"state_sha256":"c10b576b979462440a71a503690d212df8f6b03091f848de33887d53df2db3c0"}