{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EHR4BJ5ZEKM3JEQN3CYHO7Y3GO","short_pith_number":"pith:EHR4BJ5Z","canonical_record":{"source":{"id":"1201.0648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:44:23Z","cross_cats_sorted":[],"title_canon_sha256":"e86dcdc7873788a386086ecd5d9944ea284697fe4726cfb5db79408b5adcce92","abstract_canon_sha256":"55bb10b00d8b0b415423e11fb0e9c426b05dbc3370e822510b25ecb5b7761a7e"},"schema_version":"1.0"},"canonical_sha256":"21e3c0a7b92299b4920dd8b0777f1b33b9401c540731ffce188918d5ee814a96","source":{"kind":"arxiv","id":"1201.0648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0648","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0648v1","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0648","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"EHR4BJ5ZEKM3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EHR4BJ5ZEKM3JEQN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EHR4BJ5Z","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EHR4BJ5ZEKM3JEQN3CYHO7Y3GO","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:44:23Z","cross_cats_sorted":[],"title_canon_sha256":"e86dcdc7873788a386086ecd5d9944ea284697fe4726cfb5db79408b5adcce92","abstract_canon_sha256":"55bb10b00d8b0b415423e11fb0e9c426b05dbc3370e822510b25ecb5b7761a7e"},"schema_version":"1.0"},"canonical_sha256":"21e3c0a7b92299b4920dd8b0777f1b33b9401c540731ffce188918d5ee814a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:16.986134Z","signature_b64":"IFOYRgIfcBv9jDkgFrvIw3F+QaSO4AKAVrvhGO2ZIwbT9oDtxiveqZSkUZPLcdgdOJkA7WS9oL8IhHIm1737Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21e3c0a7b92299b4920dd8b0777f1b33b9401c540731ffce188918d5ee814a96","last_reissued_at":"2026-05-18T04:05:16.985478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:16.985478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0648","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":"2026-05-18T04:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IglGiP/l3uAg6wvTAMp/IkAWmanXl7wiD8Z9bFvjv99LoCTKbxvAoKRsbiU4dL4ZqGEcz8CBgc+OpinrJalNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:07:15.999364Z"},"content_sha256":"e9d72d006e0481af91e8ef2ec0cd8c22a5378986a848cbe7fcfe6177a7b31004","schema_version":"1.0","event_id":"sha256:e9d72d006e0481af91e8ef2ec0cd8c22a5378986a848cbe7fcfe6177a7b31004"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EHR4BJ5ZEKM3JEQN3CYHO7Y3GO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The local non-homogeneous Tb theorem for vector-valued functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antti V. V\\\"ah\\\"akangas, Tuomas P. Hyt\\\"onen","submitted_at":"2012-01-03T14:44:23Z","abstract_excerpt":"We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function lattice with the UMD (unconditional martingale differences) property'. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0648","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":"2026-05-18T04:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUA4GlPeGW+j85ELpX9QtCGSTSnDw6387TgyD4ypcuvvBPfAUdwxD5WfV4r4SZ4SGhpj4IbpqZFj1zOEZw7UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:07:15.999711Z"},"content_sha256":"cb25e13215c6e4b7be49f53f7b56b4b0d414b2b565376b54c0207d0c886dcca4","schema_version":"1.0","event_id":"sha256:cb25e13215c6e4b7be49f53f7b56b4b0d414b2b565376b54c0207d0c886dcca4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/bundle.json","state_url":"https://pith.science/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/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":"2026-06-04T10:07:16Z","links":{"resolver":"https://pith.science/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO","bundle":"https://pith.science/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/bundle.json","state":"https://pith.science/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHR4BJ5ZEKM3JEQN3CYHO7Y3GO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EHR4BJ5ZEKM3JEQN3CYHO7Y3GO","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":"55bb10b00d8b0b415423e11fb0e9c426b05dbc3370e822510b25ecb5b7761a7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:44:23Z","title_canon_sha256":"e86dcdc7873788a386086ecd5d9944ea284697fe4726cfb5db79408b5adcce92"},"schema_version":"1.0","source":{"id":"1201.0648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0648","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0648v1","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0648","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"EHR4BJ5ZEKM3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EHR4BJ5ZEKM3JEQN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EHR4BJ5Z","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:cb25e13215c6e4b7be49f53f7b56b4b0d414b2b565376b54c0207d0c886dcca4","target":"graph","created_at":"2026-05-18T04:05:16Z","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 extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function lattice with the UMD (unconditional martingale differences) property'. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local","authors_text":"Antti V. V\\\"ah\\\"akangas, Tuomas P. Hyt\\\"onen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:44:23Z","title":"The local non-homogeneous Tb theorem for vector-valued functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0648","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:e9d72d006e0481af91e8ef2ec0cd8c22a5378986a848cbe7fcfe6177a7b31004","target":"record","created_at":"2026-05-18T04:05:16Z","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":"55bb10b00d8b0b415423e11fb0e9c426b05dbc3370e822510b25ecb5b7761a7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:44:23Z","title_canon_sha256":"e86dcdc7873788a386086ecd5d9944ea284697fe4726cfb5db79408b5adcce92"},"schema_version":"1.0","source":{"id":"1201.0648","kind":"arxiv","version":1}},"canonical_sha256":"21e3c0a7b92299b4920dd8b0777f1b33b9401c540731ffce188918d5ee814a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21e3c0a7b92299b4920dd8b0777f1b33b9401c540731ffce188918d5ee814a96","first_computed_at":"2026-05-18T04:05:16.985478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:16.985478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFOYRgIfcBv9jDkgFrvIw3F+QaSO4AKAVrvhGO2ZIwbT9oDtxiveqZSkUZPLcdgdOJkA7WS9oL8IhHIm1737Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:16.986134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d72d006e0481af91e8ef2ec0cd8c22a5378986a848cbe7fcfe6177a7b31004","sha256:cb25e13215c6e4b7be49f53f7b56b4b0d414b2b565376b54c0207d0c886dcca4"],"state_sha256":"910af2e7742bf2ae48665d4a2c515cb5a4e28ca9d7293c424756c883f969cc89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gVQ4FdsJaanVGgj4jdAIPgA95pQTOkn87GEsBT79pxywmgCCaqB6uGbtW/kAn41/jpPxM5NnGMpuAjbfU0HaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:07:16.001676Z","bundle_sha256":"3aab4c1758222369f8deff7eebc33b6689b23511a01044534140a7101a400221"}}