{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CNS5CUKKF4A7V4RK3TOQ6CDRAK","short_pith_number":"pith:CNS5CUKK","canonical_record":{"source":{"id":"1612.03028","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-09T14:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"581e100df345d8fccd7658024f0c64a95823f324b90a7144297579203c91cffc","abstract_canon_sha256":"38f16229deeb1f3886a99ea4756909f294b9ac9ceb5a273d7d6cc83b3d89b536"},"schema_version":"1.0"},"canonical_sha256":"1365d1514a2f01faf22adcdd0f087102bda435d75f1da355f55c793f533bf816","source":{"kind":"arxiv","id":"1612.03028","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03028","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03028v2","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03028","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"CNS5CUKKF4A7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CNS5CUKKF4A7V4RK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CNS5CUKK","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CNS5CUKKF4A7V4RK3TOQ6CDRAK","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03028","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-09T14:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"581e100df345d8fccd7658024f0c64a95823f324b90a7144297579203c91cffc","abstract_canon_sha256":"38f16229deeb1f3886a99ea4756909f294b9ac9ceb5a273d7d6cc83b3d89b536"},"schema_version":"1.0"},"canonical_sha256":"1365d1514a2f01faf22adcdd0f087102bda435d75f1da355f55c793f533bf816","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:55.272449Z","signature_b64":"gF39HScQ6dY3aduaqIG1vYs+H9NCqRQoeQImOycIg0icXUgYh+l50SXWUKpEKzgoNkjygqkTBqLXwXVox2pkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1365d1514a2f01faf22adcdd0f087102bda435d75f1da355f55c793f533bf816","last_reissued_at":"2026-05-18T00:46:55.272005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:55.272005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03028","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WY6AkzHbWMh7mF8P17RyD8uoYbI7TjaMkftUwRtIZVaUzAG+FvS0dVCDxrCt9/3vYZj/dbnEDg1Lq+EqI0kXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:31:07.346157Z"},"content_sha256":"296dd1a03b7206354954e2bb90412a0d6903d77e73f5a1cd504781cb24265d09","schema_version":"1.0","event_id":"sha256:296dd1a03b7206354954e2bb90412a0d6903d77e73f5a1cd504781cb24265d09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CNS5CUKKF4A7V4RK3TOQ6CDRAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive sparse domination of variational Carleson operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Francesco Di Plinio, Gennady N. Uraltsev, Yen Q. Do","submitted_at":"2016-12-09T14:07:57Z","abstract_excerpt":"Due to its nonlocal nature, the $r$-variation norm Carleson operator $C_r$ does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome this difficulty and prove that the dual form to $C_r$ can be dominated by a positive sparse form involving $L^p$ averages. Our result strengthens the $L^p$ estimates by Oberlin et. al. As a corollary, we obtain quantitative weighted norm inequalities improving on previous results by Do and Lacey. Our proof relies on the localized outer $L^p$-embeddings of Di Plinio-Ou and Uraltsev."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03028","kind":"arxiv","version":2},"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":"2026-05-18T00:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKvRK+8GPY5cVETZX/y21kegy6+pwonIGBi/LCTfA9+WqOPKFlfJaDfpwLJZoa42SRkMQlNUgiH56uqzSW1JCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:31:07.346516Z"},"content_sha256":"47022bd5c427dd02cefafc4874b963b522742dfa9294f92932c8468a0185df83","schema_version":"1.0","event_id":"sha256:47022bd5c427dd02cefafc4874b963b522742dfa9294f92932c8468a0185df83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/bundle.json","state_url":"https://pith.science/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/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":"2026-06-05T08:31:07Z","links":{"resolver":"https://pith.science/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK","bundle":"https://pith.science/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/bundle.json","state":"https://pith.science/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNS5CUKKF4A7V4RK3TOQ6CDRAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CNS5CUKKF4A7V4RK3TOQ6CDRAK","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":"38f16229deeb1f3886a99ea4756909f294b9ac9ceb5a273d7d6cc83b3d89b536","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-09T14:07:57Z","title_canon_sha256":"581e100df345d8fccd7658024f0c64a95823f324b90a7144297579203c91cffc"},"schema_version":"1.0","source":{"id":"1612.03028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03028","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03028v2","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03028","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"CNS5CUKKF4A7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CNS5CUKKF4A7V4RK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CNS5CUKK","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:47022bd5c427dd02cefafc4874b963b522742dfa9294f92932c8468a0185df83","target":"graph","created_at":"2026-05-18T00:46:55Z","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":"Due to its nonlocal nature, the $r$-variation norm Carleson operator $C_r$ does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome this difficulty and prove that the dual form to $C_r$ can be dominated by a positive sparse form involving $L^p$ averages. Our result strengthens the $L^p$ estimates by Oberlin et. al. As a corollary, we obtain quantitative weighted norm inequalities improving on previous results by Do and Lacey. Our proof relies on the localized outer $L^p$-embeddings of Di Plinio-Ou and Uraltsev.","authors_text":"Francesco Di Plinio, Gennady N. Uraltsev, Yen Q. Do","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-09T14:07:57Z","title":"Positive sparse domination of variational Carleson operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03028","kind":"arxiv","version":2},"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":"sha256:296dd1a03b7206354954e2bb90412a0d6903d77e73f5a1cd504781cb24265d09","target":"record","created_at":"2026-05-18T00:46:55Z","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":"38f16229deeb1f3886a99ea4756909f294b9ac9ceb5a273d7d6cc83b3d89b536","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-09T14:07:57Z","title_canon_sha256":"581e100df345d8fccd7658024f0c64a95823f324b90a7144297579203c91cffc"},"schema_version":"1.0","source":{"id":"1612.03028","kind":"arxiv","version":2}},"canonical_sha256":"1365d1514a2f01faf22adcdd0f087102bda435d75f1da355f55c793f533bf816","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1365d1514a2f01faf22adcdd0f087102bda435d75f1da355f55c793f533bf816","first_computed_at":"2026-05-18T00:46:55.272005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:55.272005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gF39HScQ6dY3aduaqIG1vYs+H9NCqRQoeQImOycIg0icXUgYh+l50SXWUKpEKzgoNkjygqkTBqLXwXVox2pkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:55.272449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:296dd1a03b7206354954e2bb90412a0d6903d77e73f5a1cd504781cb24265d09","sha256:47022bd5c427dd02cefafc4874b963b522742dfa9294f92932c8468a0185df83"],"state_sha256":"5f5e29e11c24c36d659ecbb5113dcb253008a196c9d04298bcbe2df1c28d94de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DllKdM/pWEgXDjjj3D/q7vfrXJlAMWuAydLkhPMeAcmcqFfL7AoC6g6LQNGvFqphZKYG/UxmpCeVPfOoHdLsCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:31:07.348714Z","bundle_sha256":"c75958dfeb99d5a84b789f18c023949d2d63e07afa90e1cf3ae11e443ecdfdcb"}}