{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FUWN2Z7KPPJDMQVP7XGL4QPU5O","short_pith_number":"pith:FUWN2Z7K","canonical_record":{"source":{"id":"1512.02400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-08T11:01:47Z","cross_cats_sorted":[],"title_canon_sha256":"a43db990b76b42fd515624a09d787cba2390aa96334309426de89b6c4592433b","abstract_canon_sha256":"5d3bcfb187982a673af6c917514c1ba07274ef9b14f49d63c571ab50c5c742d3"},"schema_version":"1.0"},"canonical_sha256":"2d2cdd67ea7bd23642affdccbe41f4eb8e21c39a6f47f2ced339f8626d67202f","source":{"kind":"arxiv","id":"1512.02400","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02400","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02400v3","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02400","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"FUWN2Z7KPPJD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FUWN2Z7KPPJDMQVP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FUWN2Z7K","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FUWN2Z7KPPJDMQVP7XGL4QPU5O","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-08T11:01:47Z","cross_cats_sorted":[],"title_canon_sha256":"a43db990b76b42fd515624a09d787cba2390aa96334309426de89b6c4592433b","abstract_canon_sha256":"5d3bcfb187982a673af6c917514c1ba07274ef9b14f49d63c571ab50c5c742d3"},"schema_version":"1.0"},"canonical_sha256":"2d2cdd67ea7bd23642affdccbe41f4eb8e21c39a6f47f2ced339f8626d67202f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.042823Z","signature_b64":"+vICFgdtgOmF+a+2dJhZjaeHPsolPNeuUpDUNRv2AYwsQZuELE4ZtAS1elYR/8RLxMqFhK124L3jTMDfNdV+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2cdd67ea7bd23642affdccbe41f4eb8e21c39a6f47f2ced339f8626d67202f","last_reissued_at":"2026-05-18T00:06:44.042449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.042449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02400","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNXymM5y/klV3pyZsLmnWAGWyWoiGZGOreQKSHfqCqxdEqgHblYQwC3NDhQY/BFE+80wVp7grR6mqBQvBUSgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:49:46.382865Z"},"content_sha256":"f4f76db3cab3db24ea8ba29e21a0649c74eb57eacf7e8e4899637002c071b957","schema_version":"1.0","event_id":"sha256:f4f76db3cab3db24ea8ba29e21a0649c74eb57eacf7e8e4899637002c071b957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FUWN2Z7KPPJDMQVP7XGL4QPU5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New bounds for bilinear Calder\\'on-Zygmund operators and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Mahdi Hormozi, Wendol\\'in Dami\\'an","submitted_at":"2015-12-08T11:01:47Z","abstract_excerpt":"In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hyt\\\"onen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_{\\infty}$ constants inspired in the Fujii-Wilson and Hrus\\v{c}\\v{e}v classical constants. These estimates have many new applications including mixed bounds for multilinear Calder\\'on--Zygmund op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02400","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gp3L/S/EnIeNwqn/FTmhqoDgNnXstf55JITnB2BKZ4LVSwo4B6pkxHKW0/x3v2e4xcN13TYc8tFMc2ViqeqPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:49:46.383616Z"},"content_sha256":"9b9d9e78ab2baf9f2ae3678f500c3339f0c8116bb7b5f38a9e1cbe84eff08724","schema_version":"1.0","event_id":"sha256:9b9d9e78ab2baf9f2ae3678f500c3339f0c8116bb7b5f38a9e1cbe84eff08724"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/bundle.json","state_url":"https://pith.science/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/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":"2026-05-26T00:49:46Z","links":{"resolver":"https://pith.science/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O","bundle":"https://pith.science/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/bundle.json","state":"https://pith.science/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUWN2Z7KPPJDMQVP7XGL4QPU5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FUWN2Z7KPPJDMQVP7XGL4QPU5O","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":"5d3bcfb187982a673af6c917514c1ba07274ef9b14f49d63c571ab50c5c742d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-08T11:01:47Z","title_canon_sha256":"a43db990b76b42fd515624a09d787cba2390aa96334309426de89b6c4592433b"},"schema_version":"1.0","source":{"id":"1512.02400","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02400","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02400v3","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02400","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"FUWN2Z7KPPJD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FUWN2Z7KPPJDMQVP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FUWN2Z7K","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:9b9d9e78ab2baf9f2ae3678f500c3339f0c8116bb7b5f38a9e1cbe84eff08724","target":"graph","created_at":"2026-05-18T00:06:44Z","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":"In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hyt\\\"onen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_{\\infty}$ constants inspired in the Fujii-Wilson and Hrus\\v{c}\\v{e}v classical constants. These estimates have many new applications including mixed bounds for multilinear Calder\\'on--Zygmund op","authors_text":"Kangwei Li, Mahdi Hormozi, Wendol\\'in Dami\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-08T11:01:47Z","title":"New bounds for bilinear Calder\\'on-Zygmund operators and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02400","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:f4f76db3cab3db24ea8ba29e21a0649c74eb57eacf7e8e4899637002c071b957","target":"record","created_at":"2026-05-18T00:06:44Z","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":"5d3bcfb187982a673af6c917514c1ba07274ef9b14f49d63c571ab50c5c742d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-08T11:01:47Z","title_canon_sha256":"a43db990b76b42fd515624a09d787cba2390aa96334309426de89b6c4592433b"},"schema_version":"1.0","source":{"id":"1512.02400","kind":"arxiv","version":3}},"canonical_sha256":"2d2cdd67ea7bd23642affdccbe41f4eb8e21c39a6f47f2ced339f8626d67202f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d2cdd67ea7bd23642affdccbe41f4eb8e21c39a6f47f2ced339f8626d67202f","first_computed_at":"2026-05-18T00:06:44.042449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.042449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vICFgdtgOmF+a+2dJhZjaeHPsolPNeuUpDUNRv2AYwsQZuELE4ZtAS1elYR/8RLxMqFhK124L3jTMDfNdV+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.042823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02400","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f76db3cab3db24ea8ba29e21a0649c74eb57eacf7e8e4899637002c071b957","sha256:9b9d9e78ab2baf9f2ae3678f500c3339f0c8116bb7b5f38a9e1cbe84eff08724"],"state_sha256":"f5e69106de23a381ce0410b2e47a88aa176bd8e75fda2d74485b2b42494b5b49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVFZz5pV/P5nSH0JjUQZiGLWrYnuK59siRUQh5OiA4WYxMa679SEGjMQ0B4dVcwONBkZC1ZoKHMB3Cacbn11AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:49:46.387629Z","bundle_sha256":"320a90fc8e221e3d978ce79267bf6afa686d728fe84f198ffef7939d5ea234bb"}}