{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AWHBL3TC32N4MTIXYFSZ7KKWXB","short_pith_number":"pith:AWHBL3TC","canonical_record":{"source":{"id":"1704.05577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"6cebea56bbacab30994634cf18c1639727e97cb857eadb478e35a4bfa49a2504","abstract_canon_sha256":"4e30f95e1d83ba034a7a9de417fc0d187b3e25e024940a7e0e0ebb127b329fed"},"schema_version":"1.0"},"canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","source":{"kind":"arxiv","id":"1704.05577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05577","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05577v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05577","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"AWHBL3TC32N4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWHBL3TC32N4MTIX","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWHBL3TC","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AWHBL3TC32N4MTIXYFSZ7KKWXB","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"6cebea56bbacab30994634cf18c1639727e97cb857eadb478e35a4bfa49a2504","abstract_canon_sha256":"4e30f95e1d83ba034a7a9de417fc0d187b3e25e024940a7e0e0ebb127b329fed"},"schema_version":"1.0"},"canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.073258Z","signature_b64":"Zyxg4qaiOWZxG6Y9UuT4Fko3U6ncXdfuTf5yac7ftSxMEJ4dCyS+Zj3Ky0m/M//Gy/rUIte9QQwy3RGFHDOlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","last_reissued_at":"2026-05-18T00:46:07.072706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.072706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05577","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0egg1bWNDejWqwsfhs6x/zWCfcqVfQHglp6DDGxP4Jfl5FCWKqOVeLgLRnM8IH1Qcqu/wO1Ab3YDRYkRK5KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:58:35.976311Z"},"content_sha256":"4bd80142806d93b1da67421246022ac61d2c7191ee71bba7fd8eb921cdbca8de","schema_version":"1.0","event_id":"sha256:4bd80142806d93b1da67421246022ac61d2c7191ee71bba7fd8eb921cdbca8de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AWHBL3TC32N4MTIXYFSZ7KKWXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BMO estimates for stochastic singular integral operators and its application to PDEs with L\\'{e}vy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-04-19T01:57:44Z","abstract_excerpt":"In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. Following the idea of \\cite{Kim}, we obtain the $q$-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05577","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPL2xZm+X8Esf2LpKap3gnv5meMTYCm6fFQLkSPXKhbnZfm9p7UXw0WMV/aMpj6qBVLFtOub1pmszvzt/1GdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:58:35.976771Z"},"content_sha256":"65c194dc75af45facfbd56dc96c5647e6ce6c3bec7935cd1d762e64388d126f3","schema_version":"1.0","event_id":"sha256:65c194dc75af45facfbd56dc96c5647e6ce6c3bec7935cd1d762e64388d126f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/bundle.json","state_url":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/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":"2026-05-25T11:58:35Z","links":{"resolver":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB","bundle":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/bundle.json","state":"https://pith.science/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWHBL3TC32N4MTIXYFSZ7KKWXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AWHBL3TC32N4MTIXYFSZ7KKWXB","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":"4e30f95e1d83ba034a7a9de417fc0d187b3e25e024940a7e0e0ebb127b329fed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","title_canon_sha256":"6cebea56bbacab30994634cf18c1639727e97cb857eadb478e35a4bfa49a2504"},"schema_version":"1.0","source":{"id":"1704.05577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05577","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05577v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05577","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"AWHBL3TC32N4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWHBL3TC32N4MTIX","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWHBL3TC","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:65c194dc75af45facfbd56dc96c5647e6ce6c3bec7935cd1d762e64388d126f3","target":"graph","created_at":"2026-05-18T00:46:07Z","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 paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. Following the idea of \\cite{Kim}, we obtain the $q$-th","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","title":"BMO estimates for stochastic singular integral operators and its application to PDEs with L\\'{e}vy noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05577","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":"sha256:4bd80142806d93b1da67421246022ac61d2c7191ee71bba7fd8eb921cdbca8de","target":"record","created_at":"2026-05-18T00:46:07Z","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":"4e30f95e1d83ba034a7a9de417fc0d187b3e25e024940a7e0e0ebb127b329fed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T01:57:44Z","title_canon_sha256":"6cebea56bbacab30994634cf18c1639727e97cb857eadb478e35a4bfa49a2504"},"schema_version":"1.0","source":{"id":"1704.05577","kind":"arxiv","version":1}},"canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"058e15ee62de9bc64d17c1659fa956b859421e129d742da3d8ed837edb6e92d1","first_computed_at":"2026-05-18T00:46:07.072706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.072706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zyxg4qaiOWZxG6Y9UuT4Fko3U6ncXdfuTf5yac7ftSxMEJ4dCyS+Zj3Ky0m/M//Gy/rUIte9QQwy3RGFHDOlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.073258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bd80142806d93b1da67421246022ac61d2c7191ee71bba7fd8eb921cdbca8de","sha256:65c194dc75af45facfbd56dc96c5647e6ce6c3bec7935cd1d762e64388d126f3"],"state_sha256":"7aa1a151c9dc86b60c764eaebbc2fb8e3f8cbe5731b0f743d900a03ecb610fd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T697Ks17mXeTxOwGdQ8JH7vsFCK7eZJ+nuAM2cWywKKl3W3HXIq2FY7qaUNMWcyKNAGKrx+9FDp0m23BCpXFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T11:58:35.980120Z","bundle_sha256":"9d4310753fd7af6e2431dea8669c12414867fc78cba8f2817d18fa90926f0cc6"}}