{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CTOOLWA252U3RY466RE4SED3II","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":"3ef44642034fa7297af6c2757f3545eb766f79aa63d1b08cf8747bb2c494e015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-20T22:03:47Z","title_canon_sha256":"148ac958c90eb18199c007e983e4f14cbc93364f3852143cea1066f31035dd37"},"schema_version":"1.0","source":{"id":"1312.6163","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6163","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6163v4","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6163","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"CTOOLWA252U3","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CTOOLWA252U3RY46","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CTOOLWA2","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:c4e7d6483e468af0e8b17f553348fffea3f68db63f2c0281f03843ece9ab1606","target":"graph","created_at":"2026-05-18T01:14:36Z","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":"Fix an integer $ n$ and number $d$, $ 0< d\\neq n-1 \\leq n$, and two weights $ w$ and $ \\sigma $ on $ \\mathbb R ^{n}$. We two extra conditions (1) no common point masses and (2) the two weights separately are not concentrated on a set of codimension one, uniformly over locations and scales. (This condition holds for doubling weights.) Then, we characterize the two weight inequality for the $ d$-dimensional Riesz transform on $ \\mathbb R ^{n}$, \\begin{equation*} \\sup_{0< a < b < \\infty}\\left\\lVert \\int_{a < \\lvert x-y\\rvert < b} f (y) \\frac {x-y} {\\lvert x-y\\rvert ^{d+1}} \\; \\sigma (dy) \\right\\r","authors_text":"Brett D. Wick, Michael T. Lacey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-20T22:03:47Z","title":"Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6163","kind":"arxiv","version":4},"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:c70951118954fa16c8bb770672aa89897c15ef07aa8cf2248408fae63cd22167","target":"record","created_at":"2026-05-18T01:14:36Z","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":"3ef44642034fa7297af6c2757f3545eb766f79aa63d1b08cf8747bb2c494e015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-20T22:03:47Z","title_canon_sha256":"148ac958c90eb18199c007e983e4f14cbc93364f3852143cea1066f31035dd37"},"schema_version":"1.0","source":{"id":"1312.6163","kind":"arxiv","version":4}},"canonical_sha256":"14dce5d81aeea9b8e39ef449c9107b42180ce32e245500b1339ae2fbef87846d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14dce5d81aeea9b8e39ef449c9107b42180ce32e245500b1339ae2fbef87846d","first_computed_at":"2026-05-18T01:14:36.351434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.351434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vexwuV/v/sSgpLyov/wh5YUF7KKhUHzcti85KyyqdlyHC563OTqSB3mDOvW4IoXhvqC+pzETYcswT3S7XZbcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.352163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6163","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c70951118954fa16c8bb770672aa89897c15ef07aa8cf2248408fae63cd22167","sha256:c4e7d6483e468af0e8b17f553348fffea3f68db63f2c0281f03843ece9ab1606"],"state_sha256":"c1098410c32e61f6dcce0a04e5a550ab3544a464f7b01b9f2b6017ad86e46fc3"}