{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6IUKIVMJGT5QZHDF3UNSOKSHAJ","short_pith_number":"pith:6IUKIVMJ","schema_version":"1.0","canonical_sha256":"f228a4558934fb0c9c65dd1b272a4702639f33b9a8220945a7819f854d090b16","source":{"kind":"arxiv","id":"2405.11969","version":3},"attestation_state":"computed","paper":{"title":"Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Beom-seok Han, Daehan Park, Jae-Hwan Choi","submitted_at":"2024-05-20T11:48:13Z","abstract_excerpt":"This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions in mixed norm $L_q(L_p)$-spaces. We introduce a new condition (strongly reinforced Dalang's condition) on colored noise, which facilitates a deeper understanding of the complicated relation between nonlinearities and stochastic forces. Additionally, we establish the space-time H\\\"older type regularity of solutions."},"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":"2405.11969","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-20T11:48:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cbf7a4f9e12600501c1e7191e9fa364fb3814b6c9440a539fd7c990a42c4ab5e","abstract_canon_sha256":"3c710f8abfa417e7019ac9c2a0d7bd8bab387cc0d46910b49df0d0a5cdba5961"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:42.578913Z","signature_b64":"2YOSuTO5nthAVAO0q/evm5FDo4pGOctfv+96fzqwdAxbDOBXxbCBxWK9CA8B8C7Ahx+xPeHW3Ay80fJ5lLTgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f228a4558934fb0c9c65dd1b272a4702639f33b9a8220945a7819f854d090b16","last_reissued_at":"2026-07-05T12:03:42.578480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:42.578480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Beom-seok Han, Daehan Park, Jae-Hwan Choi","submitted_at":"2024-05-20T11:48:13Z","abstract_excerpt":"This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions in mixed norm $L_q(L_p)$-spaces. We introduce a new condition (strongly reinforced Dalang's condition) on colored noise, which facilitates a deeper understanding of the complicated relation between nonlinearities and stochastic forces. Additionally, we establish the space-time H\\\"older type regularity of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11969","kind":"arxiv","version":3},"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/2405.11969/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":"2405.11969","created_at":"2026-07-05T12:03:42.578541+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.11969v3","created_at":"2026-07-05T12:03:42.578541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11969","created_at":"2026-07-05T12:03:42.578541+00:00"},{"alias_kind":"pith_short_12","alias_value":"6IUKIVMJGT5Q","created_at":"2026-07-05T12:03:42.578541+00:00"},{"alias_kind":"pith_short_16","alias_value":"6IUKIVMJGT5QZHDF","created_at":"2026-07-05T12:03:42.578541+00:00"},{"alias_kind":"pith_short_8","alias_value":"6IUKIVMJ","created_at":"2026-07-05T12:03:42.578541+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.17166","citing_title":"The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\\sigma}$ open sets","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ","json":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ.json","graph_json":"https://pith.science/api/pith-number/6IUKIVMJGT5QZHDF3UNSOKSHAJ/graph.json","events_json":"https://pith.science/api/pith-number/6IUKIVMJGT5QZHDF3UNSOKSHAJ/events.json","paper":"https://pith.science/paper/6IUKIVMJ"},"agent_actions":{"view_html":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ","download_json":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ.json","view_paper":"https://pith.science/paper/6IUKIVMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.11969&json=true","fetch_graph":"https://pith.science/api/pith-number/6IUKIVMJGT5QZHDF3UNSOKSHAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6IUKIVMJGT5QZHDF3UNSOKSHAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ/action/storage_attestation","attest_author":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ/action/author_attestation","sign_citation":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ/action/citation_signature","submit_replication":"https://pith.science/pith/6IUKIVMJGT5QZHDF3UNSOKSHAJ/action/replication_record"}},"created_at":"2026-07-05T12:03:42.578541+00:00","updated_at":"2026-07-05T12:03:42.578541+00:00"}