{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TNU4NAW5DDN4J7KF3DAXSAA2ON","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":"8497cc0d895e7c833782dcd5e7bea8e70bf2201a318289927521875eb89edb3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-13T19:49:12Z","title_canon_sha256":"b83576a3808a992209394273aa4cf923200ae80ec6b61a74a773c533d4a9981d"},"schema_version":"1.0","source":{"id":"1310.3507","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3507","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3507v4","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3507","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"TNU4NAW5DDN4","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TNU4NAW5DDN4J7KF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TNU4NAW5","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:af2b315e00ad74c1a180559bc05345ee1c34f5db81ab49a686eaff889051971f","target":"graph","created_at":"2026-05-18T02:56:05Z","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 `separated bump conjecture' of Cruz-Uribe & Perez, and Cruz-Uribe & Reznikov & Volberg. In the L^p setting, we formulate a stronger version of this conjecture, and show that under it, a two weight inequality holds for all CZOs. When p=2, this is the result of Nazarov & Reznikov & Volberg (1306.2653). Our argument is based on stopping time arguments and the extra hypothesis is used in a clear-cut and seemingly essential way. This argument could be of some help in searching for a counterexample to the conjecture.","authors_text":"Michael T Lacey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-13T19:49:12Z","title":"On the Separated Bumps Conjecture for Calderon-Zygmund Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3507","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:de4117ad40d9f243b66f44a3025e0ea56361862e0c14f44737d17e75aee7a9ec","target":"record","created_at":"2026-05-18T02:56:05Z","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":"8497cc0d895e7c833782dcd5e7bea8e70bf2201a318289927521875eb89edb3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-13T19:49:12Z","title_canon_sha256":"b83576a3808a992209394273aa4cf923200ae80ec6b61a74a773c533d4a9981d"},"schema_version":"1.0","source":{"id":"1310.3507","kind":"arxiv","version":4}},"canonical_sha256":"9b69c682dd18dbc4fd45d8c179001a7374be0f4bad2968c7c035d94f62c587e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b69c682dd18dbc4fd45d8c179001a7374be0f4bad2968c7c035d94f62c587e5","first_computed_at":"2026-05-18T02:56:05.076451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:05.076451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOhLYHhQjCapIworSlSetSxcWoI8qRTLYcNf2getAK4SatvI3cRXOZErXcXQFcoO8kHKyxdW4DjPNd5kumZ9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:05.076865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3507","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de4117ad40d9f243b66f44a3025e0ea56361862e0c14f44737d17e75aee7a9ec","sha256:af2b315e00ad74c1a180559bc05345ee1c34f5db81ab49a686eaff889051971f"],"state_sha256":"7c1775bde1de430d272b00d64e7bea4a1ea3177997e7ca15b53688a674a0acce"}