{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:F5O7O57AEKKO66B23SMZMADVWQ","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":"dc3455728020c86901213ab7c0d621b6ae75f9f9ed2fc65c9d1320ef10fc426e","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-14T14:26:30Z","title_canon_sha256":"5c05eee240335ce8c639e59647183734d4fe82524d013f3d77bdf1aed32ae0a9"},"schema_version":"1.0","source":{"id":"math/0205156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205156","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205156v1","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205156","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"F5O7O57AEKKO","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_16","alias_value":"F5O7O57AEKKO66B2","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_8","alias_value":"F5O7O57A","created_at":"2026-07-04T14:36:12Z"}],"graph_snapshots":[{"event_id":"sha256:4003a3d43a440ec76f5543c009d79608948eb0a4200bb8d32122e599493b5994","target":"graph","created_at":"2026-07-04T14:36:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0205156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that some singular maximal functions and singular Radon transforms satisfy a weak type $L\\log\\log L$ inequality. Examples include the maximal function and Hilbert transform associated to averages along a parabola. The weak type inequality yields pointwise convergence results for functions which are locally in $L\\log\\log L$.","authors_text":"Andreas Seeger, James Wright, Terence Tao","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2002-05-14T14:26:30Z","title":"Singular maximal functions and Radon transforms near L^1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205156","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":"sha256:340e875ffcb31c77e4cafc4c0591e2e6cb8b0a7ea7ac0cd9c3e8df15ca5cf59a","target":"record","created_at":"2026-07-04T14:36:12Z","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":"dc3455728020c86901213ab7c0d621b6ae75f9f9ed2fc65c9d1320ef10fc426e","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-14T14:26:30Z","title_canon_sha256":"5c05eee240335ce8c639e59647183734d4fe82524d013f3d77bdf1aed32ae0a9"},"schema_version":"1.0","source":{"id":"math/0205156","kind":"arxiv","version":1}},"canonical_sha256":"2f5df777e02294ef783adc99960075b43bde0c0c0d2e8fe2558c3577881e7573","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f5df777e02294ef783adc99960075b43bde0c0c0d2e8fe2558c3577881e7573","first_computed_at":"2026-07-04T14:36:12.354974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:12.354974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDAiklfcfJ1/yjFA7gTJTTuaaWnHnZ+k3SfxEN1fcrUL9R6smsWvZiKmT4icRtW2V00VXrDtRq0eSl38eTMGDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:12.355342Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:340e875ffcb31c77e4cafc4c0591e2e6cb8b0a7ea7ac0cd9c3e8df15ca5cf59a","sha256:4003a3d43a440ec76f5543c009d79608948eb0a4200bb8d32122e599493b5994"],"state_sha256":"064d3f7095226c3b2154cdce5007576ca2cf2c8f23070157d92fcea19698776d"}