{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RUIAGEU6225WLEYPDTKC55XVCA","short_pith_number":"pith:RUIAGEU6","canonical_record":{"source":{"id":"1507.04032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"8c98909434d23c36ea9e7356cb58fb8e286691a732555ac28f436ba58d16949a","abstract_canon_sha256":"e88fe098904e1bb6e897146c1b3058be4b448a49dda88da5307d66301ba89007"},"schema_version":"1.0"},"canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","source":{"kind":"arxiv","id":"1507.04032","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04032","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04032v2","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04032","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"RUIAGEU6225W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUIAGEU6225WLEYP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUIAGEU6","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RUIAGEU6225WLEYPDTKC55XVCA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"8c98909434d23c36ea9e7356cb58fb8e286691a732555ac28f436ba58d16949a","abstract_canon_sha256":"e88fe098904e1bb6e897146c1b3058be4b448a49dda88da5307d66301ba89007"},"schema_version":"1.0"},"canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:33.851895Z","signature_b64":"Y98C5KyRWVcOoCR3dq+a4rYYmJc4CA2HLENfIE3xvPeCnbPDnJEkJeMwCfVSGLpDnQbZ8XG5dtW3Bwb4KZczCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","last_reissued_at":"2026-05-18T00:40:33.851220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:33.851220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04032","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5/h9b5AuUnc0y/0FmXZXj4/9+d9Rda2PtTObZJVgJ0lnpb64895NYICw/RuO4+eeDH+Lz/AA5VuI99e4cAoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:48:22.475859Z"},"content_sha256":"94cdb6ba036f2b8782ebf67fd98b8067a2601d1b0cd440be696ade122b134f38","schema_version":"1.0","event_id":"sha256:94cdb6ba036f2b8782ebf67fd98b8067a2601d1b0cd440be696ade122b134f38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RUIAGEU6225WLEYPDTKC55XVCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hyun-Kyoung Kwon, Joshua Isralowitz, Sandra Pott","submitted_at":"2015-07-14T21:29:00Z","abstract_excerpt":"Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \\infty$, and $T$ be any of the Riesz transforms. We will characterize the boundedness of the commutator $[T, B]$ on $L^p(W)$ in terms of the membership of $B$ in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on $L^p(W)$ via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04032","kind":"arxiv","version":2},"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":"2026-05-18T00:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3Fzba0ukJEieLB4VeQpMTXnS/6GtOq+aMdaKBfDkbtD0LF4WvgmFPh8fDen5chqdbPcWfg/2qbPdXJPjQNMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:48:22.476496Z"},"content_sha256":"9ce84a550b2f28a1e079526fdecc750599b23a3893c52f0d66ee02b326168280","schema_version":"1.0","event_id":"sha256:9ce84a550b2f28a1e079526fdecc750599b23a3893c52f0d66ee02b326168280"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUIAGEU6225WLEYPDTKC55XVCA/bundle.json","state_url":"https://pith.science/pith/RUIAGEU6225WLEYPDTKC55XVCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUIAGEU6225WLEYPDTKC55XVCA/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":"2026-05-26T15:48:22Z","links":{"resolver":"https://pith.science/pith/RUIAGEU6225WLEYPDTKC55XVCA","bundle":"https://pith.science/pith/RUIAGEU6225WLEYPDTKC55XVCA/bundle.json","state":"https://pith.science/pith/RUIAGEU6225WLEYPDTKC55XVCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUIAGEU6225WLEYPDTKC55XVCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RUIAGEU6225WLEYPDTKC55XVCA","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":"e88fe098904e1bb6e897146c1b3058be4b448a49dda88da5307d66301ba89007","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","title_canon_sha256":"8c98909434d23c36ea9e7356cb58fb8e286691a732555ac28f436ba58d16949a"},"schema_version":"1.0","source":{"id":"1507.04032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04032","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04032v2","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04032","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"RUIAGEU6225W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUIAGEU6225WLEYP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUIAGEU6","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:9ce84a550b2f28a1e079526fdecc750599b23a3893c52f0d66ee02b326168280","target":"graph","created_at":"2026-05-18T00:40:33Z","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":"Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \\infty$, and $T$ be any of the Riesz transforms. We will characterize the boundedness of the commutator $[T, B]$ on $L^p(W)$ in terms of the membership of $B$ in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on $L^p(W)$ via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to pro","authors_text":"Hyun-Kyoung Kwon, Joshua Isralowitz, Sandra Pott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","title":"Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04032","kind":"arxiv","version":2},"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":"sha256:94cdb6ba036f2b8782ebf67fd98b8067a2601d1b0cd440be696ade122b134f38","target":"record","created_at":"2026-05-18T00:40:33Z","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":"e88fe098904e1bb6e897146c1b3058be4b448a49dda88da5307d66301ba89007","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","title_canon_sha256":"8c98909434d23c36ea9e7356cb58fb8e286691a732555ac28f436ba58d16949a"},"schema_version":"1.0","source":{"id":"1507.04032","kind":"arxiv","version":2}},"canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","first_computed_at":"2026-05-18T00:40:33.851220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:33.851220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y98C5KyRWVcOoCR3dq+a4rYYmJc4CA2HLENfIE3xvPeCnbPDnJEkJeMwCfVSGLpDnQbZ8XG5dtW3Bwb4KZczCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:33.851895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94cdb6ba036f2b8782ebf67fd98b8067a2601d1b0cd440be696ade122b134f38","sha256:9ce84a550b2f28a1e079526fdecc750599b23a3893c52f0d66ee02b326168280"],"state_sha256":"6302b6527a2fc7930c26fe50b1e55f13a339ce9b5a651f0b5ea44232614311b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oCSqKqHxunfhaRUtd9LE5gNwv0nUT6O1XAEXycAYJUs0G7yKm7BagJ8EyEyjX69z5aKLy8mXRKgTIlB2azWWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:48:22.479461Z","bundle_sha256":"7bda4e81f3cdf90a17a662c2545571b26aff84fe30a287ef277c878cac88feae"}}