{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:IOUK5BIOCBYGCDRAPOKJ7APUVL","short_pith_number":"pith:IOUK5BIO","canonical_record":{"source":{"id":"0910.1142","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-10-07T01:01:11Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"83f1aa0cb98f9e50a3aa744caba50b8620ec3892b0337358c15748fb3d26ff41","abstract_canon_sha256":"f3a486597deda73ebe163e372c5094599a8a6638c23c89031c2a5b50bf59deb1"},"schema_version":"1.0"},"canonical_sha256":"43a8ae850e1070610e207b949f81f4aadc7112b8fdfaaeb444f2b4c8e57b3e6e","source":{"kind":"arxiv","id":"0910.1142","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1142","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1142v3","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1142","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"IOUK5BIOCBYG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IOUK5BIOCBYGCDRA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IOUK5BIO","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:IOUK5BIOCBYGCDRAPOKJ7APUVL","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1142","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-10-07T01:01:11Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"83f1aa0cb98f9e50a3aa744caba50b8620ec3892b0337358c15748fb3d26ff41","abstract_canon_sha256":"f3a486597deda73ebe163e372c5094599a8a6638c23c89031c2a5b50bf59deb1"},"schema_version":"1.0"},"canonical_sha256":"43a8ae850e1070610e207b949f81f4aadc7112b8fdfaaeb444f2b4c8e57b3e6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:33.085286Z","signature_b64":"/DeCuw0Q+BrnbPoVcdwecSioAkpiCg79ZM7Csp1t/FKWNy689oCnsALqmsgao8OcPPJeCyqGHZ4N4noazlnBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43a8ae850e1070610e207b949f81f4aadc7112b8fdfaaeb444f2b4c8e57b3e6e","last_reissued_at":"2026-05-18T03:49:33.084452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:33.084452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1142","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WZw1zUkswFOxVQTJxdn9w9PdM/+IqVRrUKR+8YZUgva0RZxpjmUYSCcO/QUraO0CfwRJ6rAb4NQuWl9jz72CCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:12.031954Z"},"content_sha256":"c74aef5f24b12fc0aadae888a5813ab32d69ea3800ec54b657ccebd24b9bc745","schema_version":"1.0","event_id":"sha256:c74aef5f24b12fc0aadae888a5813ab32d69ea3800ec54b657ccebd24b9bc745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:IOUK5BIOCBYGCDRAPOKJ7APUVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Alexander Volberg, Brett D. Wick","submitted_at":"2009-10-07T01:01:11Z","abstract_excerpt":"The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle \"Bergman--type\" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^\\sigma_2$ on the complex ball of $\\mathbb{C}^d$. In particular, we demonstrate that for any $\\sigma> 0$, the Carleson measures for the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1142","kind":"arxiv","version":3},"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":"2026-05-18T03:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iA8KEkWT2iPgUDDtDQ+EYbchXgjlxmM+wkxqodIScX9+Enqozb1RYVaVWyJs7jiIYpOo/J5m9fzCC3K+oGCICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:12.032541Z"},"content_sha256":"9c9cfb859f57e69ddd15a324630eb63deed75ddce31373da36db3ddecd1356f0","schema_version":"1.0","event_id":"sha256:9c9cfb859f57e69ddd15a324630eb63deed75ddce31373da36db3ddecd1356f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/bundle.json","state_url":"https://pith.science/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/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":"2026-05-31T23:52:12Z","links":{"resolver":"https://pith.science/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL","bundle":"https://pith.science/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/bundle.json","state":"https://pith.science/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOUK5BIOCBYGCDRAPOKJ7APUVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IOUK5BIOCBYGCDRAPOKJ7APUVL","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":"f3a486597deda73ebe163e372c5094599a8a6638c23c89031c2a5b50bf59deb1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-10-07T01:01:11Z","title_canon_sha256":"83f1aa0cb98f9e50a3aa744caba50b8620ec3892b0337358c15748fb3d26ff41"},"schema_version":"1.0","source":{"id":"0910.1142","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1142","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1142v3","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1142","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"IOUK5BIOCBYG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IOUK5BIOCBYGCDRA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IOUK5BIO","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:9c9cfb859f57e69ddd15a324630eb63deed75ddce31373da36db3ddecd1356f0","target":"graph","created_at":"2026-05-18T03:49:33Z","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":"The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle \"Bergman--type\" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^\\sigma_2$ on the complex ball of $\\mathbb{C}^d$. In particular, we demonstrate that for any $\\sigma> 0$, the Carleson measures for the sp","authors_text":"Alexander Volberg, Brett D. Wick","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-10-07T01:01:11Z","title":"Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex Ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1142","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:c74aef5f24b12fc0aadae888a5813ab32d69ea3800ec54b657ccebd24b9bc745","target":"record","created_at":"2026-05-18T03:49:33Z","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":"f3a486597deda73ebe163e372c5094599a8a6638c23c89031c2a5b50bf59deb1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-10-07T01:01:11Z","title_canon_sha256":"83f1aa0cb98f9e50a3aa744caba50b8620ec3892b0337358c15748fb3d26ff41"},"schema_version":"1.0","source":{"id":"0910.1142","kind":"arxiv","version":3}},"canonical_sha256":"43a8ae850e1070610e207b949f81f4aadc7112b8fdfaaeb444f2b4c8e57b3e6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43a8ae850e1070610e207b949f81f4aadc7112b8fdfaaeb444f2b4c8e57b3e6e","first_computed_at":"2026-05-18T03:49:33.084452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:33.084452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/DeCuw0Q+BrnbPoVcdwecSioAkpiCg79ZM7Csp1t/FKWNy689oCnsALqmsgao8OcPPJeCyqGHZ4N4noazlnBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:33.085286Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1142","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c74aef5f24b12fc0aadae888a5813ab32d69ea3800ec54b657ccebd24b9bc745","sha256:9c9cfb859f57e69ddd15a324630eb63deed75ddce31373da36db3ddecd1356f0"],"state_sha256":"d8d55253df8fe9a87f12e5a1d6870f8db20f41e0f928bd024c7d8e495320b208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6lgK1E8tGOfyrekhHemMwRxzaoID0L5D8Xr4X0AdxImj7FgGpiXKHNEiEc3ogYfheEoDvRRKxKOXA7a/d6CCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:52:12.035188Z","bundle_sha256":"4c5450c4b5304612d6873d981737accc6d4fc5971c2b2ae2a9e4513ef0528032"}}