{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5A4UEWPVQDD3VTRQOWDXG23EMC","short_pith_number":"pith:5A4UEWPV","canonical_record":{"source":{"id":"1704.05580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T02:04:18Z","cross_cats_sorted":[],"title_canon_sha256":"62ca7d2212ea75357093c819198a4e502dfb712ffdd9d2baf23209e5b361fe71","abstract_canon_sha256":"8dcb96c90a268922a025beded95460c43b27a7ca59759bcbddf3dab5a8137a79"},"schema_version":"1.0"},"canonical_sha256":"e8394259f580c7bace307587736b64608ed2d673ba42a27c46aa77162bc73d7a","source":{"kind":"arxiv","id":"1704.05580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05580","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05580v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05580","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"5A4UEWPVQDD3","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5A4UEWPVQDD3VTRQ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5A4UEWPV","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5A4UEWPVQDD3VTRQOWDXG23EMC","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T02:04:18Z","cross_cats_sorted":[],"title_canon_sha256":"62ca7d2212ea75357093c819198a4e502dfb712ffdd9d2baf23209e5b361fe71","abstract_canon_sha256":"8dcb96c90a268922a025beded95460c43b27a7ca59759bcbddf3dab5a8137a79"},"schema_version":"1.0"},"canonical_sha256":"e8394259f580c7bace307587736b64608ed2d673ba42a27c46aa77162bc73d7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.066619Z","signature_b64":"0bGnXktopxaqcXZfpQNwmgWpssha8PxEeIpNuxdIeIYH6rYQA74lcASJB+4YpHu6xFRIfWOydG7YBZrLfewyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8394259f580c7bace307587736b64608ed2d673ba42a27c46aa77162bc73d7a","last_reissued_at":"2026-05-18T00:46:07.066213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.066213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05580","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":"rFtw1VyGOhMRCgx6EsOiv25lNwJsSbXjSCnuG9B0R6mZ3yxahkWqVHUblNkbfkoiMTWJP27vL98RdDq+XAbYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:11:42.366470Z"},"content_sha256":"9fec63ccedd7b4f6ae0922c8f4067318097cd0e1a18671807cb99b4012ca0aed","schema_version":"1.0","event_id":"sha256:9fec63ccedd7b4f6ae0922c8f4067318097cd0e1a18671807cb99b4012ca0aed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5A4UEWPVQDD3VTRQOWDXG23EMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs","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":"2017-04-19T02:04:18Z","abstract_excerpt":"In this paper, we are concerned with the estimates for the moments of stochastic convolution integrals. We first deal with the stochastic singular integral operators and we aim to derive the Morrey-Campanato estimates for the $p$-moments (for $p\\ge1$). Then, by utilising the embedding theory between the Campanato space and H\\\"older space, we establish the norm of $C^{\\theta,\\theta/2}(\\bar D)$, where $\\theta\\ge0, \\bar D=\\bar G\\times[0,T]$ for arbitrarily fixed $T\\in(0,\\infty)$ and $G\\subset\\mathbb{R}^d$. As an application, we consider the following stochastic (fractional) heat equations with ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05580","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":"dBOjuw3O5HSSniFVXjI73v8uoSkBDSMNlqEtcvkqYRtNwc0HJST9sfimesIzcsOKjNtFGm/fAxe9VstCkIZrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:11:42.367210Z"},"content_sha256":"89992f37160f725f71a0ceb7c459612db818d36e71bd240886bd2d2c53d562e7","schema_version":"1.0","event_id":"sha256:89992f37160f725f71a0ceb7c459612db818d36e71bd240886bd2d2c53d562e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/bundle.json","state_url":"https://pith.science/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/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":"2026-05-25T11:11:42Z","links":{"resolver":"https://pith.science/pith/5A4UEWPVQDD3VTRQOWDXG23EMC","bundle":"https://pith.science/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/bundle.json","state":"https://pith.science/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5A4UEWPVQDD3VTRQOWDXG23EMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5A4UEWPVQDD3VTRQOWDXG23EMC","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":"8dcb96c90a268922a025beded95460c43b27a7ca59759bcbddf3dab5a8137a79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T02:04:18Z","title_canon_sha256":"62ca7d2212ea75357093c819198a4e502dfb712ffdd9d2baf23209e5b361fe71"},"schema_version":"1.0","source":{"id":"1704.05580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05580","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05580v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05580","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"5A4UEWPVQDD3","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5A4UEWPVQDD3VTRQ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5A4UEWPV","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:89992f37160f725f71a0ceb7c459612db818d36e71bd240886bd2d2c53d562e7","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 are concerned with the estimates for the moments of stochastic convolution integrals. We first deal with the stochastic singular integral operators and we aim to derive the Morrey-Campanato estimates for the $p$-moments (for $p\\ge1$). Then, by utilising the embedding theory between the Campanato space and H\\\"older space, we establish the norm of $C^{\\theta,\\theta/2}(\\bar D)$, where $\\theta\\ge0, \\bar D=\\bar G\\times[0,T]$ for arbitrarily fixed $T\\in(0,\\infty)$ and $G\\subset\\mathbb{R}^d$. As an application, we consider the following stochastic (fractional) heat equations with ad","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":"2017-04-19T02:04:18Z","title":"Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05580","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":"sha256:9fec63ccedd7b4f6ae0922c8f4067318097cd0e1a18671807cb99b4012ca0aed","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":"8dcb96c90a268922a025beded95460c43b27a7ca59759bcbddf3dab5a8137a79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T02:04:18Z","title_canon_sha256":"62ca7d2212ea75357093c819198a4e502dfb712ffdd9d2baf23209e5b361fe71"},"schema_version":"1.0","source":{"id":"1704.05580","kind":"arxiv","version":1}},"canonical_sha256":"e8394259f580c7bace307587736b64608ed2d673ba42a27c46aa77162bc73d7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8394259f580c7bace307587736b64608ed2d673ba42a27c46aa77162bc73d7a","first_computed_at":"2026-05-18T00:46:07.066213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.066213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0bGnXktopxaqcXZfpQNwmgWpssha8PxEeIpNuxdIeIYH6rYQA74lcASJB+4YpHu6xFRIfWOydG7YBZrLfewyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.066619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fec63ccedd7b4f6ae0922c8f4067318097cd0e1a18671807cb99b4012ca0aed","sha256:89992f37160f725f71a0ceb7c459612db818d36e71bd240886bd2d2c53d562e7"],"state_sha256":"c39adfb82b6839f21da1e99ffb11684041b14883699d0c6ec3f0fd8e280dc3bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJfydlAd1dZ802HiAucPXq4/0C3dv3+CA6JgGH745/Kx2uPCD8eEsr1bCUwXOSSWFdnzCbL/rKZNXvW/6nkHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T11:11:42.373706Z","bundle_sha256":"8680dc6792a695316bb8c9632410144141b3912249717f000ce86ec41e5f3d51"}}