{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KAILI4RYI2ITXDOKZO3TCIV3RD","short_pith_number":"pith:KAILI4RY","schema_version":"1.0","canonical_sha256":"5010b4723846913b8dcacbb73122bb88c0949ba7b2a939e1aa4b026d0e098de9","source":{"kind":"arxiv","id":"2501.02924","version":1},"attestation_state":"computed","paper":{"title":"Yamada-Watanabe uniqueness results for SPDEs driven by Wiener and pure jump processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Kenneth H. Karlsen, Kistosil Fahim","submitted_at":"2025-01-06T11:04:35Z","abstract_excerpt":"The Yamada-Watanabe theory provides a robust framework for understanding stochastic equations driven by Wiener processes. Despite its comprehensive treatment in the literature, the applicability of the theory to SPDEs driven by Poisson random measures or, more generally, L\\'evy processes remains significantly less explored, with only a handful of results addressing this context. In this work, we leverage a result by Kurtz to demonstrate that the existence of a martingale solution combined with pathwise uniqueness implies the existence of a unique strong solution for SPDEs driven by both a Wien"},"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":"2501.02924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-06T11:04:35Z","cross_cats_sorted":[],"title_canon_sha256":"d3fa86881797f88fde1a1547cda47425a87274789e395a8ae71e235d6eda87e9","abstract_canon_sha256":"438374063a230033998a4004a5c3fbc074fdca95576e3b87fb806c551ed24dcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:27.098111Z","signature_b64":"xWiSUX21+EppisBW2Zg3cTtvP7U0hZQRm+/tP2XNk5ERSI3ozXx/jesQj8BrgqekpKjLgpNHIx9kIBywTe9dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5010b4723846913b8dcacbb73122bb88c0949ba7b2a939e1aa4b026d0e098de9","last_reissued_at":"2026-07-05T09:57:27.097553Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:27.097553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Yamada-Watanabe uniqueness results for SPDEs driven by Wiener and pure jump processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Kenneth H. Karlsen, Kistosil Fahim","submitted_at":"2025-01-06T11:04:35Z","abstract_excerpt":"The Yamada-Watanabe theory provides a robust framework for understanding stochastic equations driven by Wiener processes. Despite its comprehensive treatment in the literature, the applicability of the theory to SPDEs driven by Poisson random measures or, more generally, L\\'evy processes remains significantly less explored, with only a handful of results addressing this context. In this work, we leverage a result by Kurtz to demonstrate that the existence of a martingale solution combined with pathwise uniqueness implies the existence of a unique strong solution for SPDEs driven by both a Wien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02924","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/2501.02924/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":"2501.02924","created_at":"2026-07-05T09:57:27.097619+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.02924v1","created_at":"2026-07-05T09:57:27.097619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.02924","created_at":"2026-07-05T09:57:27.097619+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAILI4RYI2IT","created_at":"2026-07-05T09:57:27.097619+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAILI4RYI2ITXDOK","created_at":"2026-07-05T09:57:27.097619+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAILI4RY","created_at":"2026-07-05T09:57:27.097619+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.00189","citing_title":"The Yamada-Watanabe-Engelbert theorem for SPDEs in Banach spaces","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD","json":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD.json","graph_json":"https://pith.science/api/pith-number/KAILI4RYI2ITXDOKZO3TCIV3RD/graph.json","events_json":"https://pith.science/api/pith-number/KAILI4RYI2ITXDOKZO3TCIV3RD/events.json","paper":"https://pith.science/paper/KAILI4RY"},"agent_actions":{"view_html":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD","download_json":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD.json","view_paper":"https://pith.science/paper/KAILI4RY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.02924&json=true","fetch_graph":"https://pith.science/api/pith-number/KAILI4RYI2ITXDOKZO3TCIV3RD/graph.json","fetch_events":"https://pith.science/api/pith-number/KAILI4RYI2ITXDOKZO3TCIV3RD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD/action/storage_attestation","attest_author":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD/action/author_attestation","sign_citation":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD/action/citation_signature","submit_replication":"https://pith.science/pith/KAILI4RYI2ITXDOKZO3TCIV3RD/action/replication_record"}},"created_at":"2026-07-05T09:57:27.097619+00:00","updated_at":"2026-07-05T09:57:27.097619+00:00"}