{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JWX64L6R2NEABP2BIGQTJ6UQGY","short_pith_number":"pith:JWX64L6R","canonical_record":{"source":{"id":"1104.1069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-06T11:50:57Z","cross_cats_sorted":[],"title_canon_sha256":"a8f7ae9de7bfce479ab648c974809eac8ac55f84da7df94ad6ac011c92e6c152","abstract_canon_sha256":"fae967a7e1b5b0108d48e3bd7835c7876230ab5bd711a0c76e48a292accda7a8"},"schema_version":"1.0"},"canonical_sha256":"4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21","source":{"kind":"arxiv","id":"1104.1069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1069","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1069v1","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1069","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"JWX64L6R2NEA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWX64L6R2NEABP2B","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWX64L6R","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JWX64L6R2NEABP2BIGQTJ6UQGY","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-06T11:50:57Z","cross_cats_sorted":[],"title_canon_sha256":"a8f7ae9de7bfce479ab648c974809eac8ac55f84da7df94ad6ac011c92e6c152","abstract_canon_sha256":"fae967a7e1b5b0108d48e3bd7835c7876230ab5bd711a0c76e48a292accda7a8"},"schema_version":"1.0"},"canonical_sha256":"4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:53.685722Z","signature_b64":"bPjphcLSXHtkGIkBjmQNcEW0/c9kDH0RM+GFoHcrIaXI/qDVZGkXudq4d3aYTsmVemwSgdIK44g13APB8VUmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21","last_reissued_at":"2026-05-18T04:24:53.685021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:53.685021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1069","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hy5r8O3M23296kfsa38+v1v8Cw7QO1iTeEhMRyvjNQ+ZGc/VDmlwZvxZs8uWM0G9gmR7xchfOMu966NvcaEoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T05:56:12.119037Z"},"content_sha256":"41721d72ec9f8f8de00f0ddbd2e49ca4e97daa5c1b3410110beb4347f0541d69","schema_version":"1.0","event_id":"sha256:41721d72ec9f8f8de00f0ddbd2e49ca4e97daa5c1b3410110beb4347f0541d69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JWX64L6R2NEABP2BIGQTJ6UQGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic $A_1$ bounds for commutators of singular integrals with BMO functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carmen Ortiz-Caraballo","submitted_at":"2011-04-06T11:50:57Z","abstract_excerpt":"For commutators of the form [b,T] where T is any Calderon--Zygmund operator and b is any BMO function we derive weighted quadratic type estimates in term of the A1 constant of the weight both in the Lp context or of LlogL type at the endpoint"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1069","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkIxyJH/fm2KAo+CXsrGd+BHpFLEZNqfAQp/z3g398nw6KBnsp4JkVtrPX6srr120fcxGH8D9zCsOZnx6MCbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T05:56:12.119385Z"},"content_sha256":"8d0513f95148954f9e1d06ae9f8361f1f90e1f3a5d775ccd67516b1ef1e9c597","schema_version":"1.0","event_id":"sha256:8d0513f95148954f9e1d06ae9f8361f1f90e1f3a5d775ccd67516b1ef1e9c597"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/bundle.json","state_url":"https://pith.science/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T05:56:12Z","links":{"resolver":"https://pith.science/pith/JWX64L6R2NEABP2BIGQTJ6UQGY","bundle":"https://pith.science/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/bundle.json","state":"https://pith.science/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWX64L6R2NEABP2BIGQTJ6UQGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JWX64L6R2NEABP2BIGQTJ6UQGY","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":"fae967a7e1b5b0108d48e3bd7835c7876230ab5bd711a0c76e48a292accda7a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-06T11:50:57Z","title_canon_sha256":"a8f7ae9de7bfce479ab648c974809eac8ac55f84da7df94ad6ac011c92e6c152"},"schema_version":"1.0","source":{"id":"1104.1069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1069","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1069v1","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1069","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"JWX64L6R2NEA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWX64L6R2NEABP2B","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWX64L6R","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8d0513f95148954f9e1d06ae9f8361f1f90e1f3a5d775ccd67516b1ef1e9c597","target":"graph","created_at":"2026-05-18T04:24:53Z","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 commutators of the form [b,T] where T is any Calderon--Zygmund operator and b is any BMO function we derive weighted quadratic type estimates in term of the A1 constant of the weight both in the Lp context or of LlogL type at the endpoint","authors_text":"Carmen Ortiz-Caraballo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-06T11:50:57Z","title":"Quadratic $A_1$ bounds for commutators of singular integrals with BMO functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1069","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":"sha256:41721d72ec9f8f8de00f0ddbd2e49ca4e97daa5c1b3410110beb4347f0541d69","target":"record","created_at":"2026-05-18T04:24:53Z","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":"fae967a7e1b5b0108d48e3bd7835c7876230ab5bd711a0c76e48a292accda7a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-06T11:50:57Z","title_canon_sha256":"a8f7ae9de7bfce479ab648c974809eac8ac55f84da7df94ad6ac011c92e6c152"},"schema_version":"1.0","source":{"id":"1104.1069","kind":"arxiv","version":1}},"canonical_sha256":"4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dafee2fd1d34800bf4141a134fa90360ac2d035ceb1703af3f221986947bf21","first_computed_at":"2026-05-18T04:24:53.685021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.685021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPjphcLSXHtkGIkBjmQNcEW0/c9kDH0RM+GFoHcrIaXI/qDVZGkXudq4d3aYTsmVemwSgdIK44g13APB8VUmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.685722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41721d72ec9f8f8de00f0ddbd2e49ca4e97daa5c1b3410110beb4347f0541d69","sha256:8d0513f95148954f9e1d06ae9f8361f1f90e1f3a5d775ccd67516b1ef1e9c597"],"state_sha256":"29164b2a4deccf80cd73bb63b4f52a31a82d544158436a386f191fe83d4f0731"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ghq3cuG8dWRXcV27vedrlU0ZG9m/ocYlr4prE4XkjvujvePIX+QC1supBbSCbt1a9XbhChrWgnVBmgNZjz8KBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T05:56:12.121175Z","bundle_sha256":"435932931ea1017db76195f38f89f0a14f22f21bccbbc571d4accb8f9b50b0d5"}}