{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VAPTHI4ZPZBTHAKNYC45FFBQI4","short_pith_number":"pith:VAPTHI4Z","schema_version":"1.0","canonical_sha256":"a81f33a3997e4333814dc0b9d2943047345c8693510907ec8217863f3fe22837","source":{"kind":"arxiv","id":"2206.10069","version":1},"attestation_state":"computed","paper":{"title":"Moments and asymptotics for a class of SPDEs with space-time white noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Song, Le Chen, Yuhui Guo","submitted_at":"2022-06-21T01:41:12Z","abstract_excerpt":"In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition:\n  \\begin{equation*}\n  \\left(\\partial^{\\beta}_t+\\dfrac{\\nu}{2}\\left(-\\Delta\\right)^{\\alpha / 2}\\right) u(t, x)= ~ I_{t}^{\\gamma}\\left[\\lambda u(t, x) \\dot{W}(t, x)\\right]\n  \\quad t>0,~ x\\in\\mathbb R^d,\n  \\end{equation*}\n  where $\\dot{W}$ is space-time white noise, $\\alpha>0$, $\\beta\\in(0,2]$, $\\gamma \\ge 0$, $\\lambda\\neq0$ and $\\nu>0$. The existence and uniqueness of solution in the It\\^o-Skorohod sense is obtained under Dalang"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2206.10069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-06-21T01:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"41328789e65c7229f8d95d449ce67519f043a72f767a74ad5c898ccb1aefdf84","abstract_canon_sha256":"0da97d53a2643a8fbb7cefe7f465092c664733e458c6f2b6806cba4b9e28f5e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:33:43.202545Z","signature_b64":"jHb+3BiBaHaKvURCUybVNsNERkNMAqHsW0z7J9jby4LizAPmBD/hUgQkXqYVg0cEVK54dTebRhXxWfXmvQ8wCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a81f33a3997e4333814dc0b9d2943047345c8693510907ec8217863f3fe22837","last_reissued_at":"2026-07-05T04:33:43.202128Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:33:43.202128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moments and asymptotics for a class of SPDEs with space-time white noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Song, Le Chen, Yuhui Guo","submitted_at":"2022-06-21T01:41:12Z","abstract_excerpt":"In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition:\n  \\begin{equation*}\n  \\left(\\partial^{\\beta}_t+\\dfrac{\\nu}{2}\\left(-\\Delta\\right)^{\\alpha / 2}\\right) u(t, x)= ~ I_{t}^{\\gamma}\\left[\\lambda u(t, x) \\dot{W}(t, x)\\right]\n  \\quad t>0,~ x\\in\\mathbb R^d,\n  \\end{equation*}\n  where $\\dot{W}$ is space-time white noise, $\\alpha>0$, $\\beta\\in(0,2]$, $\\gamma \\ge 0$, $\\lambda\\neq0$ and $\\nu>0$. The existence and uniqueness of solution in the It\\^o-Skorohod sense is obtained under Dalang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10069","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.10069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2206.10069","created_at":"2026-07-05T04:33:43.202188+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.10069v1","created_at":"2026-07-05T04:33:43.202188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.10069","created_at":"2026-07-05T04:33:43.202188+00:00"},{"alias_kind":"pith_short_12","alias_value":"VAPTHI4ZPZBT","created_at":"2026-07-05T04:33:43.202188+00:00"},{"alias_kind":"pith_short_16","alias_value":"VAPTHI4ZPZBTHAKN","created_at":"2026-07-05T04:33:43.202188+00:00"},{"alias_kind":"pith_short_8","alias_value":"VAPTHI4Z","created_at":"2026-07-05T04:33:43.202188+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2310.18726","citing_title":"Stochastic partial differential equations associated with Feller processes","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4","json":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4.json","graph_json":"https://pith.science/api/pith-number/VAPTHI4ZPZBTHAKNYC45FFBQI4/graph.json","events_json":"https://pith.science/api/pith-number/VAPTHI4ZPZBTHAKNYC45FFBQI4/events.json","paper":"https://pith.science/paper/VAPTHI4Z"},"agent_actions":{"view_html":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4","download_json":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4.json","view_paper":"https://pith.science/paper/VAPTHI4Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.10069&json=true","fetch_graph":"https://pith.science/api/pith-number/VAPTHI4ZPZBTHAKNYC45FFBQI4/graph.json","fetch_events":"https://pith.science/api/pith-number/VAPTHI4ZPZBTHAKNYC45FFBQI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4/action/storage_attestation","attest_author":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4/action/author_attestation","sign_citation":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4/action/citation_signature","submit_replication":"https://pith.science/pith/VAPTHI4ZPZBTHAKNYC45FFBQI4/action/replication_record"}},"created_at":"2026-07-05T04:33:43.202188+00:00","updated_at":"2026-07-05T04:33:43.202188+00:00"}