{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5HJSO24TASQAET7UZL2B3BAP5S","short_pith_number":"pith:5HJSO24T","canonical_record":{"source":{"id":"1109.6396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T04:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcf1f29a024ba47c00d2da5c23017359fb220002be7e55bf6f10c76c248480df","abstract_canon_sha256":"22fb968a538f0e67cf6d970777edbeea2d97f859853002da4136bda964664c02"},"schema_version":"1.0"},"canonical_sha256":"e9d3276b9304a0024ff4caf41d840fec9eefd922d8b4ce48946336fb6b6194fb","source":{"kind":"arxiv","id":"1109.6396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6396","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6396v1","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6396","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"5HJSO24TASQA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5HJSO24TASQAET7U","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5HJSO24T","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5HJSO24TASQAET7UZL2B3BAP5S","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T04:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcf1f29a024ba47c00d2da5c23017359fb220002be7e55bf6f10c76c248480df","abstract_canon_sha256":"22fb968a538f0e67cf6d970777edbeea2d97f859853002da4136bda964664c02"},"schema_version":"1.0"},"canonical_sha256":"e9d3276b9304a0024ff4caf41d840fec9eefd922d8b4ce48946336fb6b6194fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:28.904614Z","signature_b64":"mxUksBG3ESaVd4TVXKJkGccsUUSR5HfvTMj8eD6vA4TW1pABFLyKbL2XxDfojrdP7kofopMKMhlaurBKj6lhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9d3276b9304a0024ff4caf41d840fec9eefd922d8b4ce48946336fb6b6194fb","last_reissued_at":"2026-05-18T01:22:28.904140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:28.904140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6396","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":"2026-05-18T01:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vr5rXpm5w+jumFSMnUbzVC1J1Uhxrav+x9PWAI8MPtgtLdCxS02FIBVRo0MS5+YP3XNE+h4Nitg4/EhTHOkpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:14:11.610404Z"},"content_sha256":"00eceb8ee744c61ca2970f3a836afa292d999ce02702ccd470c7ebaf5e8a7f83","schema_version":"1.0","event_id":"sha256:00eceb8ee744c61ca2970f3a836afa292d999ce02702ccd470c7ebaf5e8a7f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5HJSO24TASQAET7UZL2B3BAP5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^p$ estimates for the Hilbert transforms along a one-variable vector field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christoph Thiele, Michael Bateman","submitted_at":"2011-09-29T04:31:42Z","abstract_excerpt":"Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, $L^2$ whenever $v$ is Lipschitz. We establish a wide range of $L^p$ estimates for this operator when $v$ is a measurable, non-vanishing, one-variable vector field in $\\bbr ^2$. Aside from an $L^2$ estimate following from a simple trick with Carleson's theorem, these estimates were unknown previously. This paper is closely related to a recent paper of the first author (\\cite{B2})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6396","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":"2026-05-18T01:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGIzcKOut3RORWrGocZ60TTz5lvk9YlXdGrEhPzyZPsTF08ZW5Y516pFKUz1Jrwr6nCLLONfCvrWbn1Me2JoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:14:11.611082Z"},"content_sha256":"9d0bf528bb53ca6236df7c62a0fcb378f41146e831ab2a85351c9f55152e9c0d","schema_version":"1.0","event_id":"sha256:9d0bf528bb53ca6236df7c62a0fcb378f41146e831ab2a85351c9f55152e9c0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HJSO24TASQAET7UZL2B3BAP5S/bundle.json","state_url":"https://pith.science/pith/5HJSO24TASQAET7UZL2B3BAP5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HJSO24TASQAET7UZL2B3BAP5S/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":"2026-06-11T23:14:11Z","links":{"resolver":"https://pith.science/pith/5HJSO24TASQAET7UZL2B3BAP5S","bundle":"https://pith.science/pith/5HJSO24TASQAET7UZL2B3BAP5S/bundle.json","state":"https://pith.science/pith/5HJSO24TASQAET7UZL2B3BAP5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HJSO24TASQAET7UZL2B3BAP5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5HJSO24TASQAET7UZL2B3BAP5S","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":"22fb968a538f0e67cf6d970777edbeea2d97f859853002da4136bda964664c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T04:31:42Z","title_canon_sha256":"bcf1f29a024ba47c00d2da5c23017359fb220002be7e55bf6f10c76c248480df"},"schema_version":"1.0","source":{"id":"1109.6396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6396","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6396v1","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6396","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"5HJSO24TASQA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5HJSO24TASQAET7U","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5HJSO24T","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:9d0bf528bb53ca6236df7c62a0fcb378f41146e831ab2a85351c9f55152e9c0d","target":"graph","created_at":"2026-05-18T01:22:28Z","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":"Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, $L^2$ whenever $v$ is Lipschitz. We establish a wide range of $L^p$ estimates for this operator when $v$ is a measurable, non-vanishing, one-variable vector field in $\\bbr ^2$. Aside from an $L^2$ estimate following from a simple trick with Carleson's theorem, these estimates were unknown previously. This paper is closely related to a recent paper of the first author (\\cite{B2}).","authors_text":"Christoph Thiele, Michael Bateman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T04:31:42Z","title":"$L^p$ estimates for the Hilbert transforms along a one-variable vector field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6396","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":"sha256:00eceb8ee744c61ca2970f3a836afa292d999ce02702ccd470c7ebaf5e8a7f83","target":"record","created_at":"2026-05-18T01:22:28Z","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":"22fb968a538f0e67cf6d970777edbeea2d97f859853002da4136bda964664c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T04:31:42Z","title_canon_sha256":"bcf1f29a024ba47c00d2da5c23017359fb220002be7e55bf6f10c76c248480df"},"schema_version":"1.0","source":{"id":"1109.6396","kind":"arxiv","version":1}},"canonical_sha256":"e9d3276b9304a0024ff4caf41d840fec9eefd922d8b4ce48946336fb6b6194fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9d3276b9304a0024ff4caf41d840fec9eefd922d8b4ce48946336fb6b6194fb","first_computed_at":"2026-05-18T01:22:28.904140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:28.904140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mxUksBG3ESaVd4TVXKJkGccsUUSR5HfvTMj8eD6vA4TW1pABFLyKbL2XxDfojrdP7kofopMKMhlaurBKj6lhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:28.904614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00eceb8ee744c61ca2970f3a836afa292d999ce02702ccd470c7ebaf5e8a7f83","sha256:9d0bf528bb53ca6236df7c62a0fcb378f41146e831ab2a85351c9f55152e9c0d"],"state_sha256":"f18eb3560ddeed5f7c96520ad6babf4223a5fbb46cb793f25f91579d87ce3999"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"di06t+4Boh1QDqAKa1sTtnr22sLlq9azb8xyBtetfS+XYu0AGZPBxg/KEHzIqSd2RSCzd1SOimTw49kx7EaOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:14:11.614965Z","bundle_sha256":"71e6ef29df5692fb247f8b0e1ead3598cf733f2d62f86d7e4abad74ce4d5ad6c"}}