{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QFBSUFUKVZ3Q5RE2P5TDPDWFW4","short_pith_number":"pith:QFBSUFUK","canonical_record":{"source":{"id":"1105.4504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T17:01:31Z","cross_cats_sorted":[],"title_canon_sha256":"ac93264cd075a7aed7b0fd8c6282ae733f1e12464c36c6244c85a276acba982f","abstract_canon_sha256":"895300a0c5ed826de57589cebbbe04c7e329de82e25052a53961dc6baa20efb2"},"schema_version":"1.0"},"canonical_sha256":"81432a168aae770ec49a7f66378ec5b71b515105ab4b93d66ceadc5c50eb50bd","source":{"kind":"arxiv","id":"1105.4504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4504","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4504v3","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4504","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"QFBSUFUKVZ3Q","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QFBSUFUKVZ3Q5RE2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QFBSUFUK","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QFBSUFUKVZ3Q5RE2P5TDPDWFW4","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T17:01:31Z","cross_cats_sorted":[],"title_canon_sha256":"ac93264cd075a7aed7b0fd8c6282ae733f1e12464c36c6244c85a276acba982f","abstract_canon_sha256":"895300a0c5ed826de57589cebbbe04c7e329de82e25052a53961dc6baa20efb2"},"schema_version":"1.0"},"canonical_sha256":"81432a168aae770ec49a7f66378ec5b71b515105ab4b93d66ceadc5c50eb50bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.480450Z","signature_b64":"2rCJpiQ6aQZqtpMMqJKExf3gi9da9NYB/G1wWsaz7pBTop663Hbl2oruDp9ffWKZypVYEVKOaCQICMRAuu7lAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81432a168aae770ec49a7f66378ec5b71b515105ab4b93d66ceadc5c50eb50bd","last_reissued_at":"2026-05-17T23:54:27.479753Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.479753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4504","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QW7p00X71/rOFxJ8Ja33euoueLCoSXYEjOG/b924nSG6bipe0g4cf66yPvyTnrR9kkZh/xp4l7C8+XD8S3qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:04:52.877244Z"},"content_sha256":"71ff9095250b396e0dc680f3fab8147748e1d3ce40d1ecb2dc981671e0f77c67","schema_version":"1.0","event_id":"sha256:71ff9095250b396e0dc680f3fab8147748e1d3ce40d1ecb2dc981671e0f77c67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QFBSUFUKVZ3Q5RE2P5TDPDWFW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Polynomial Carleson Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Lie","submitted_at":"2011-05-19T17:01:31Z","abstract_excerpt":"We prove affirmatively the one dimensional case of a conjecture of Stein regarding the $L^p$-boundedness of the Polynomial Carleson operator, for $1<p<\\infty$.\n  The proof is based on two new ideas: i) developing a framework for \\emph{higher-order wave-packet analysis} that is consistent with the time-frequency analysis of the (generalized) Carleson operator, and ii) a new tile discretization of the time-frequency plane that has the major consequence of \\emph{eliminating the exceptional sets} from the analysis of the Carleson operator. As a further consequence, we are able to provide the full "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4504","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZ7kEXwRFsbUE1ZXnKV+MXbAOSx6JJf837Orxa/wvtMeApYnIZMOxD3eBtL02A+l0k9wtYKtUt1wq9h3QLi/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:04:52.877617Z"},"content_sha256":"92d2d8bdd957649e4b6c75819032b88dc2b82f5b8e2787f6ba3829dc074624cb","schema_version":"1.0","event_id":"sha256:92d2d8bdd957649e4b6c75819032b88dc2b82f5b8e2787f6ba3829dc074624cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/bundle.json","state_url":"https://pith.science/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/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":"2026-06-01T06:04:52Z","links":{"resolver":"https://pith.science/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4","bundle":"https://pith.science/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/bundle.json","state":"https://pith.science/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFBSUFUKVZ3Q5RE2P5TDPDWFW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QFBSUFUKVZ3Q5RE2P5TDPDWFW4","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":"895300a0c5ed826de57589cebbbe04c7e329de82e25052a53961dc6baa20efb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T17:01:31Z","title_canon_sha256":"ac93264cd075a7aed7b0fd8c6282ae733f1e12464c36c6244c85a276acba982f"},"schema_version":"1.0","source":{"id":"1105.4504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4504","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4504v3","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4504","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"QFBSUFUKVZ3Q","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QFBSUFUKVZ3Q5RE2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QFBSUFUK","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:92d2d8bdd957649e4b6c75819032b88dc2b82f5b8e2787f6ba3829dc074624cb","target":"graph","created_at":"2026-05-17T23:54:27Z","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 prove affirmatively the one dimensional case of a conjecture of Stein regarding the $L^p$-boundedness of the Polynomial Carleson operator, for $1<p<\\infty$.\n  The proof is based on two new ideas: i) developing a framework for \\emph{higher-order wave-packet analysis} that is consistent with the time-frequency analysis of the (generalized) Carleson operator, and ii) a new tile discretization of the time-frequency plane that has the major consequence of \\emph{eliminating the exceptional sets} from the analysis of the Carleson operator. As a further consequence, we are able to provide the full ","authors_text":"Victor Lie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T17:01:31Z","title":"The Polynomial Carleson Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4504","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":"sha256:71ff9095250b396e0dc680f3fab8147748e1d3ce40d1ecb2dc981671e0f77c67","target":"record","created_at":"2026-05-17T23:54:27Z","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":"895300a0c5ed826de57589cebbbe04c7e329de82e25052a53961dc6baa20efb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T17:01:31Z","title_canon_sha256":"ac93264cd075a7aed7b0fd8c6282ae733f1e12464c36c6244c85a276acba982f"},"schema_version":"1.0","source":{"id":"1105.4504","kind":"arxiv","version":3}},"canonical_sha256":"81432a168aae770ec49a7f66378ec5b71b515105ab4b93d66ceadc5c50eb50bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81432a168aae770ec49a7f66378ec5b71b515105ab4b93d66ceadc5c50eb50bd","first_computed_at":"2026-05-17T23:54:27.479753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:27.479753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2rCJpiQ6aQZqtpMMqJKExf3gi9da9NYB/G1wWsaz7pBTop663Hbl2oruDp9ffWKZypVYEVKOaCQICMRAuu7lAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:27.480450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71ff9095250b396e0dc680f3fab8147748e1d3ce40d1ecb2dc981671e0f77c67","sha256:92d2d8bdd957649e4b6c75819032b88dc2b82f5b8e2787f6ba3829dc074624cb"],"state_sha256":"8d7d418e5e699ae21148d7f85d04095e69d234ce11b9d26a998a0ac2ad8f1417"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8+SAOLTodbnyGa5bZ99H2DMp9T4zhb6qHtPAWRPbOJJgwgxly/C7cZKntMSwgG+u7/ztL3g3GnWcJEd3OBuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:04:52.879799Z","bundle_sha256":"aa97bbfe73a3aad8caedab1f0ecc5be09d7ca6faee4f1d62d4613b5c45453e86"}}