{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BLMXDUOMIDIYCSZNPJ5DSCDJDC","short_pith_number":"pith:BLMXDUOM","canonical_record":{"source":{"id":"1709.08261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-24T21:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"7e72e4e9d2c1c487fd0360e0fb2650aa7d16c39128d8f3f713a42916c8d9dc91","abstract_canon_sha256":"6fb3077b87bcd1247a48bdb47d2d198612172475dff29deec3c847416585f693"},"schema_version":"1.0"},"canonical_sha256":"0ad971d1cc40d1814b2d7a7a390869189ab15bb5fa1b53075eb73443f64ea288","source":{"kind":"arxiv","id":"1709.08261","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08261","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08261v1","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08261","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"BLMXDUOMIDIY","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BLMXDUOMIDIYCSZN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BLMXDUOM","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BLMXDUOMIDIYCSZNPJ5DSCDJDC","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-24T21:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"7e72e4e9d2c1c487fd0360e0fb2650aa7d16c39128d8f3f713a42916c8d9dc91","abstract_canon_sha256":"6fb3077b87bcd1247a48bdb47d2d198612172475dff29deec3c847416585f693"},"schema_version":"1.0"},"canonical_sha256":"0ad971d1cc40d1814b2d7a7a390869189ab15bb5fa1b53075eb73443f64ea288","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:26.000613Z","signature_b64":"bs706+oZKqCtPg1eFXj0rcE8AiKIO1RUKuh3ESDGZGOKTfRBAQ//IQXX6mWGXDSN2an1hO3GBNo/5NTVow56DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ad971d1cc40d1814b2d7a7a390869189ab15bb5fa1b53075eb73443f64ea288","last_reissued_at":"2026-05-18T00:34:26.000216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:26.000216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08261","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":"2026-05-18T00:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sINP+5hnV6jti5VO/3PLCO0DRtlrw4GTFEhXBtzmm0Sx1Jb0nHIo9M3eqHtBaMBjR0rarROi6WwXQWIzptUeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:57:40.083944Z"},"content_sha256":"1323577e19fec7dd1ae22f95f6226a5a322deacbe09db944ad83a0f196e0d40c","schema_version":"1.0","event_id":"sha256:1323577e19fec7dd1ae22f95f6226a5a322deacbe09db944ad83a0f196e0d40c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BLMXDUOMIDIYCSZNPJ5DSCDJDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on weighted bounds for rough singular integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei K. Lerner","submitted_at":"2017-09-24T21:22:35Z","abstract_excerpt":"We show that the $L^2(w)$ operator norm of the composition $M\\!\\circ T_{\\Omega}$, where $M$ is the maximal operator and $T_{\\Omega}$ is a rough homogeneous singular integral with angular part $\\Omega\\in L^{\\infty}(S^{n-1})$, depends quadratically on $[w]_{A_2}$, and this dependence is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08261","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":"2026-05-18T00:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7DWIkfiZSm18EncXXqdpo4/Z+RJjgNIqOiN721S1zskT+fr51TYMguBYucozX97SbL/utvS63XiizEMjVwcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:57:40.084280Z"},"content_sha256":"4352fe6c45dbc695a74bfbd6ba9fd9cc485d3b6ad2083efa1120132e4e76cc56","schema_version":"1.0","event_id":"sha256:4352fe6c45dbc695a74bfbd6ba9fd9cc485d3b6ad2083efa1120132e4e76cc56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/bundle.json","state_url":"https://pith.science/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/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":"2026-06-20T02:57:40Z","links":{"resolver":"https://pith.science/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC","bundle":"https://pith.science/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/bundle.json","state":"https://pith.science/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLMXDUOMIDIYCSZNPJ5DSCDJDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BLMXDUOMIDIYCSZNPJ5DSCDJDC","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":"6fb3077b87bcd1247a48bdb47d2d198612172475dff29deec3c847416585f693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-24T21:22:35Z","title_canon_sha256":"7e72e4e9d2c1c487fd0360e0fb2650aa7d16c39128d8f3f713a42916c8d9dc91"},"schema_version":"1.0","source":{"id":"1709.08261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08261","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08261v1","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08261","created_at":"2026-05-18T00:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"BLMXDUOMIDIY","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BLMXDUOMIDIYCSZN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BLMXDUOM","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:4352fe6c45dbc695a74bfbd6ba9fd9cc485d3b6ad2083efa1120132e4e76cc56","target":"graph","created_at":"2026-05-18T00:34:26Z","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 show that the $L^2(w)$ operator norm of the composition $M\\!\\circ T_{\\Omega}$, where $M$ is the maximal operator and $T_{\\Omega}$ is a rough homogeneous singular integral with angular part $\\Omega\\in L^{\\infty}(S^{n-1})$, depends quadratically on $[w]_{A_2}$, and this dependence is sharp.","authors_text":"Andrei K. Lerner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-24T21:22:35Z","title":"A note on weighted bounds for rough singular integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08261","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":"sha256:1323577e19fec7dd1ae22f95f6226a5a322deacbe09db944ad83a0f196e0d40c","target":"record","created_at":"2026-05-18T00:34:26Z","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":"6fb3077b87bcd1247a48bdb47d2d198612172475dff29deec3c847416585f693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-24T21:22:35Z","title_canon_sha256":"7e72e4e9d2c1c487fd0360e0fb2650aa7d16c39128d8f3f713a42916c8d9dc91"},"schema_version":"1.0","source":{"id":"1709.08261","kind":"arxiv","version":1}},"canonical_sha256":"0ad971d1cc40d1814b2d7a7a390869189ab15bb5fa1b53075eb73443f64ea288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ad971d1cc40d1814b2d7a7a390869189ab15bb5fa1b53075eb73443f64ea288","first_computed_at":"2026-05-18T00:34:26.000216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:26.000216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bs706+oZKqCtPg1eFXj0rcE8AiKIO1RUKuh3ESDGZGOKTfRBAQ//IQXX6mWGXDSN2an1hO3GBNo/5NTVow56DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:26.000613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1323577e19fec7dd1ae22f95f6226a5a322deacbe09db944ad83a0f196e0d40c","sha256:4352fe6c45dbc695a74bfbd6ba9fd9cc485d3b6ad2083efa1120132e4e76cc56"],"state_sha256":"6f158aa2ba74e5652d312f6b39bc6f477b915189f5d91f1534c3a07c09685f71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/bCSRhRqNLep7MHW32qShuHvOyPLpkocYbwzdtGiGTrZKLc7EUKDxYM/x/QgwrBRn7I2aedsg4tqpZj6JyNCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:57:40.086215Z","bundle_sha256":"c6ff42285df234935b5c655ecaec16af51f6295858a0624e34a81cb20410a179"}}