{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6HCSANWLAGPYDVQ2CSKOQEB6IR","short_pith_number":"pith:6HCSANWL","schema_version":"1.0","canonical_sha256":"f1c52036cb019f81d61a1494e8103e444a51e6d89ae0af7e7483107a43095f71","source":{"kind":"arxiv","id":"1908.03490","version":2},"attestation_state":"computed","paper":{"title":"Comparing the stochastic nonlinear wave and heat equations: a case study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Tadahiro Oh","submitted_at":"2019-08-09T15:14:54Z","abstract_excerpt":"We study the two-dimensional stochastic nonlinear wave equation (SNLW) and stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional derivative (of order $\\alpha > 0$) of a space-time white noise. In particular, we show that the well-posedness theory breaks at $\\alpha = \\frac 12$ for SNLW and at $\\alpha = 1$ for SNLH. This provides a first example showing that SNLW behaves less favorably than SNLH. (i) As for SNLW, Deya (2020) essentially proved its local well-posedness for $0 < \\alpha < \\frac 12$. We first revisit this argument and establish multilinear s"},"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":"1908.03490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-09T15:14:54Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6c7e3431f21243096233499074201b5c010fdc2c8ba862fdd619df0bb29bb7b4","abstract_canon_sha256":"b2f8de0820dd97cc93c031c2ec6c59741247188d2c38ba70fd011cbdf1b7a405"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:00:08.719269Z","signature_b64":"SBzhNxLNx4DW091/bMegbm9k7ILnOp1lHG4BOrVRbCsnNVQfMdVHxx7dVWG1R7o8k83Hv8raU/Zasu3sBfQgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1c52036cb019f81d61a1494e8103e444a51e6d89ae0af7e7483107a43095f71","last_reissued_at":"2026-07-05T02:00:08.718911Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:00:08.718911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparing the stochastic nonlinear wave and heat equations: a case study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Tadahiro Oh","submitted_at":"2019-08-09T15:14:54Z","abstract_excerpt":"We study the two-dimensional stochastic nonlinear wave equation (SNLW) and stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional derivative (of order $\\alpha > 0$) of a space-time white noise. In particular, we show that the well-posedness theory breaks at $\\alpha = \\frac 12$ for SNLW and at $\\alpha = 1$ for SNLH. This provides a first example showing that SNLW behaves less favorably than SNLH. (i) As for SNLW, Deya (2020) essentially proved its local well-posedness for $0 < \\alpha < \\frac 12$. We first revisit this argument and establish multilinear s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03490","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03490/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":"1908.03490","created_at":"2026-07-05T02:00:08.718976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03490v2","created_at":"2026-07-05T02:00:08.718976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03490","created_at":"2026-07-05T02:00:08.718976+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HCSANWLAGPY","created_at":"2026-07-05T02:00:08.718976+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HCSANWLAGPYDVQ2","created_at":"2026-07-05T02:00:08.718976+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HCSANWL","created_at":"2026-07-05T02:00:08.718976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR","json":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR.json","graph_json":"https://pith.science/api/pith-number/6HCSANWLAGPYDVQ2CSKOQEB6IR/graph.json","events_json":"https://pith.science/api/pith-number/6HCSANWLAGPYDVQ2CSKOQEB6IR/events.json","paper":"https://pith.science/paper/6HCSANWL"},"agent_actions":{"view_html":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR","download_json":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR.json","view_paper":"https://pith.science/paper/6HCSANWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03490&json=true","fetch_graph":"https://pith.science/api/pith-number/6HCSANWLAGPYDVQ2CSKOQEB6IR/graph.json","fetch_events":"https://pith.science/api/pith-number/6HCSANWLAGPYDVQ2CSKOQEB6IR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR/action/storage_attestation","attest_author":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR/action/author_attestation","sign_citation":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR/action/citation_signature","submit_replication":"https://pith.science/pith/6HCSANWLAGPYDVQ2CSKOQEB6IR/action/replication_record"}},"created_at":"2026-07-05T02:00:08.718976+00:00","updated_at":"2026-07-05T02:00:08.718976+00:00"}