{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IZXQ2KBJUF63LNRU64DXLRVA5L","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":"f15a1f37b7070e3f42d777124a01cd518be4f1adf1704c8f807b52812eb42311","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-13T12:18:37Z","title_canon_sha256":"61e2e85757a9f65364ee5f076ace52f5d413a55b9dc72e0846ed160bf1e916e9"},"schema_version":"1.0","source":{"id":"1006.2530","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2530","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2530v3","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2530","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"IZXQ2KBJUF63","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZXQ2KBJUF63LNRU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZXQ2KBJ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a58ba3d89d257d8dd7404f2f831bf82e6fd35d34fbbe2983734a9db8693b7cc7","target":"graph","created_at":"2026-05-18T04:25:37Z","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 a Calderon-Zygmund operator T on d-dimensional space, that has a sufficiently smooth kernel, we prove that for any 1< p \\le 2, and weight w in A_p, that the maximal truncations T_* of T map L^p(w) to weak-L^p(w), with norm bounded by the A_p characteristic of w to the first power. This result combined with the (deep) recent result of Perez-Treil-Volberg, shows that the strong-type of T on L^2(w) is bounded by A_2 characteristic of w to the first power. (It is well-known that L^2 is the critical case for the strong type estimate.) Both results are sharp, aside from the number of derivatives","authors_text":"Armen Vagharshakyan, Eric T. Sawyer, Ignacio Uriarte-Tuero, Maria Carmen Reguera, Michael T. Lacey, Tuomas P. Hyt\\\"onen","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-13T12:18:37Z","title":"Weak and Strong type $ A_p$ Estimates for Calder\\'on-Zygmund Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2530","kind":"arxiv","version":3},"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":"sha256:39eba99cda61b70d9f4315dcf6c2edeeb22d3c37a59780c05d5793bebd8e6f21","target":"record","created_at":"2026-05-18T04:25:37Z","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":"f15a1f37b7070e3f42d777124a01cd518be4f1adf1704c8f807b52812eb42311","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-13T12:18:37Z","title_canon_sha256":"61e2e85757a9f65364ee5f076ace52f5d413a55b9dc72e0846ed160bf1e916e9"},"schema_version":"1.0","source":{"id":"1006.2530","kind":"arxiv","version":3}},"canonical_sha256":"466f0d2829a17db5b634f70775c6a0eadda0f74b307818cec6ce9dd5c75dbc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"466f0d2829a17db5b634f70775c6a0eadda0f74b307818cec6ce9dd5c75dbc9d","first_computed_at":"2026-05-18T04:25:37.849377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.849377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Drm2NOJXE5pSZe2sdG173ns9Hehn2EeAJdkh1aI4+z8Csa8u1yBAdndZHWbOOnlVNy7VGxyGWwRl2cIBGdrTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.849808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2530","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39eba99cda61b70d9f4315dcf6c2edeeb22d3c37a59780c05d5793bebd8e6f21","sha256:a58ba3d89d257d8dd7404f2f831bf82e6fd35d34fbbe2983734a9db8693b7cc7"],"state_sha256":"4e57eaafac5341b71dc4683f5281215e3d40ae7ed8c704da7c378be1d02edbb7"}