{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IBVXJP3MAP2WLL4UR5CPMZMC2O","short_pith_number":"pith:IBVXJP3M","canonical_record":{"source":{"id":"1806.07263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-18T10:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"980a4a85cfe867de3cfd5d7623f179557ebca4a4d26da7e03088c21d151c2a88","abstract_canon_sha256":"7cbca18078f0473b665d6c96f21863350048a3bb7e2a815f5ba1f067b83203aa"},"schema_version":"1.0"},"canonical_sha256":"406b74bf6c03f565af948f44f66582d3ab4f4b37cc00d079d3852c69046e4d50","source":{"kind":"arxiv","id":"1806.07263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07263","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07263v2","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07263","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"IBVXJP3MAP2W","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IBVXJP3MAP2WLL4U","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IBVXJP3M","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IBVXJP3MAP2WLL4UR5CPMZMC2O","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-18T10:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"980a4a85cfe867de3cfd5d7623f179557ebca4a4d26da7e03088c21d151c2a88","abstract_canon_sha256":"7cbca18078f0473b665d6c96f21863350048a3bb7e2a815f5ba1f067b83203aa"},"schema_version":"1.0"},"canonical_sha256":"406b74bf6c03f565af948f44f66582d3ab4f4b37cc00d079d3852c69046e4d50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:59.596619Z","signature_b64":"OcUqF+n23UzlAH/N718M554FY14G/7Evidq4Pqy/5L5TpuUz6+Ktf86EnAIZEM4+c6outDEVcvSuAqlMY7Q2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"406b74bf6c03f565af948f44f66582d3ab4f4b37cc00d079d3852c69046e4d50","last_reissued_at":"2026-05-17T23:50:59.596108Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:59.596108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07263","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":"2026-05-17T23:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQfVYPjQ4MZ8uNH5fAB7lDbLip110uO+x2vKapGpxft4uWk1Ievnk70FQlvlwBdFd0SdSV6Bd6r88TcxrmnfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:44:18.732365Z"},"content_sha256":"08f0da872311afce301adef867af7bd3a76147e3cd64ad30da4ee58114199980","schema_version":"1.0","event_id":"sha256:08f0da872311afce301adef867af7bd3a76147e3cd64ad30da4ee58114199980"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IBVXJP3MAP2WLL4UR5CPMZMC2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The composition of singular integral operators with nonsmooth kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu, Yandan Zhang","submitted_at":"2018-06-18T10:17:13Z","abstract_excerpt":"Let $T_1$, $T_2$ be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi-sublinear sparse domination, the authors obtain some quantitative bounds on $L^p(\\mathbb{R}^n,\\,w)$ with $p\\in(1,\\,\\infty)$ and $w\\in A_p(\\mathbb{R}^n)$ for the composite operator $T_1T_2$. Some weighted weak type endpoint estimates are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07263","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":"2026-05-17T23:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CX4IRwJLk5F+WdrGdj+qg+unF85OdZud3yvHO0evl8+4D1DF2B7zz/f1A4jkc9/BgKFIyyPMYuomPWColQCqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:44:18.732700Z"},"content_sha256":"8a0a68434deb193b7d765485b9e82b6fccc56d6e5c40265e2e09e908ad50d36e","schema_version":"1.0","event_id":"sha256:8a0a68434deb193b7d765485b9e82b6fccc56d6e5c40265e2e09e908ad50d36e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/bundle.json","state_url":"https://pith.science/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/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":"2026-06-20T06:44:18Z","links":{"resolver":"https://pith.science/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O","bundle":"https://pith.science/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/bundle.json","state":"https://pith.science/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBVXJP3MAP2WLL4UR5CPMZMC2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IBVXJP3MAP2WLL4UR5CPMZMC2O","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":"7cbca18078f0473b665d6c96f21863350048a3bb7e2a815f5ba1f067b83203aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-18T10:17:13Z","title_canon_sha256":"980a4a85cfe867de3cfd5d7623f179557ebca4a4d26da7e03088c21d151c2a88"},"schema_version":"1.0","source":{"id":"1806.07263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07263","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07263v2","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07263","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"IBVXJP3MAP2W","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IBVXJP3MAP2WLL4U","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IBVXJP3M","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:8a0a68434deb193b7d765485b9e82b6fccc56d6e5c40265e2e09e908ad50d36e","target":"graph","created_at":"2026-05-17T23:50:59Z","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":"Let $T_1$, $T_2$ be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi-sublinear sparse domination, the authors obtain some quantitative bounds on $L^p(\\mathbb{R}^n,\\,w)$ with $p\\in(1,\\,\\infty)$ and $w\\in A_p(\\mathbb{R}^n)$ for the composite operator $T_1T_2$. Some weighted weak type endpoint estimates are also given.","authors_text":"Guoen Hu, Yandan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-18T10:17:13Z","title":"The composition of singular integral operators with nonsmooth kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07263","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":"sha256:08f0da872311afce301adef867af7bd3a76147e3cd64ad30da4ee58114199980","target":"record","created_at":"2026-05-17T23:50:59Z","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":"7cbca18078f0473b665d6c96f21863350048a3bb7e2a815f5ba1f067b83203aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-18T10:17:13Z","title_canon_sha256":"980a4a85cfe867de3cfd5d7623f179557ebca4a4d26da7e03088c21d151c2a88"},"schema_version":"1.0","source":{"id":"1806.07263","kind":"arxiv","version":2}},"canonical_sha256":"406b74bf6c03f565af948f44f66582d3ab4f4b37cc00d079d3852c69046e4d50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"406b74bf6c03f565af948f44f66582d3ab4f4b37cc00d079d3852c69046e4d50","first_computed_at":"2026-05-17T23:50:59.596108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:59.596108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OcUqF+n23UzlAH/N718M554FY14G/7Evidq4Pqy/5L5TpuUz6+Ktf86EnAIZEM4+c6outDEVcvSuAqlMY7Q2Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:59.596619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08f0da872311afce301adef867af7bd3a76147e3cd64ad30da4ee58114199980","sha256:8a0a68434deb193b7d765485b9e82b6fccc56d6e5c40265e2e09e908ad50d36e"],"state_sha256":"9ac5d0b4e8e7bc32aef74704b959e00b0a65c06b9883a6405ba35ba840499bc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUBXPyWD5Pm49g98CoSr1hC7Xy3kYM2dKie6v5qOWo9Bt0PyNIu4DTv4rdrernAe5DExQgSbaSV7uDs0N+b0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:44:18.734444Z","bundle_sha256":"5976d28350ea348a3ee7d5ffe8f844de4944be6387a3fef84e45ee0e869118d2"}}