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We show that, for all $\\alpha\\in [0,\\frac{1}{2}),$ \\[ u\\in L^2(\\Omega;W^{\\alpha,2}(0,T;\\mathsf{D}(A^{1/2}))) \\quad \\text{ if and only if }\\quad x\\in \\mathsf{D}(A^{\\alpha}). \\] In particular, there is a lack of persistence of temporal regularity from the diffusion coefficient $g$ to the solutio"},"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":"2509.07803","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-09T14:44:15Z","cross_cats_sorted":[],"title_canon_sha256":"d48ed46b88003e8328d324dfd79644c62f8b476e4abd0c8cb0107538a2fa0fe8","abstract_canon_sha256":"91d5b51202fa4a9df66727df80782c7caa9b8abc5a8c911c990a138cdb90a0a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:03:26.255304Z","signature_b64":"O88Hu7zSGN6nV3rqKwspTF7gKrH7ESPSKKsgbxtY+LBEJlu4se0Clknd3JP+okqmji7G9A8MmhZXb8NiS68WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba48c03760d94af91192164d6b7d0449887b3b9e0d86c06d5efcb9192a42c1c1","last_reissued_at":"2026-06-01T02:03:26.253954Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:03:26.253954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on a threshold for temporal regularity of stochastic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Agresti, Mark Veraar","submitted_at":"2025-09-09T14:44:15Z","abstract_excerpt":"We consider solutions to linear parabolic SPDEs of the form \\[ \\mathrm{d} u(t) + A u(t)\\, \\mathrm{d} t = g(t)\\, \\mathrm{d} \\beta, \\qquad u(0)=0, \\] where $A$ is a positive, invertible, and self-adjoint operator on a Hilbert space $X$, $\\beta$ is a one-dimensional Brownian motion, and $g(t)\\equiv x\\in X$. We show that, for all $\\alpha\\in [0,\\frac{1}{2}),$ \\[ u\\in L^2(\\Omega;W^{\\alpha,2}(0,T;\\mathsf{D}(A^{1/2}))) \\quad \\text{ if and only if }\\quad x\\in \\mathsf{D}(A^{\\alpha}). \\] In particular, there is a lack of persistence of temporal regularity from the diffusion coefficient $g$ to the solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07803","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/2509.07803/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":"2509.07803","created_at":"2026-06-01T02:03:26.254101+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07803v3","created_at":"2026-06-01T02:03:26.254101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07803","created_at":"2026-06-01T02:03:26.254101+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJEMAN3A3FFP","created_at":"2026-06-01T02:03:26.254101+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJEMAN3A3FFPSEMS","created_at":"2026-06-01T02:03:26.254101+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJEMAN3A","created_at":"2026-06-01T02:03:26.254101+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/XJEMAN3A3FFPSEMSCZGWW7IEJG","json":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG.json","graph_json":"https://pith.science/api/pith-number/XJEMAN3A3FFPSEMSCZGWW7IEJG/graph.json","events_json":"https://pith.science/api/pith-number/XJEMAN3A3FFPSEMSCZGWW7IEJG/events.json","paper":"https://pith.science/paper/XJEMAN3A"},"agent_actions":{"view_html":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG","download_json":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG.json","view_paper":"https://pith.science/paper/XJEMAN3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07803&json=true","fetch_graph":"https://pith.science/api/pith-number/XJEMAN3A3FFPSEMSCZGWW7IEJG/graph.json","fetch_events":"https://pith.science/api/pith-number/XJEMAN3A3FFPSEMSCZGWW7IEJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG/action/storage_attestation","attest_author":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG/action/author_attestation","sign_citation":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG/action/citation_signature","submit_replication":"https://pith.science/pith/XJEMAN3A3FFPSEMSCZGWW7IEJG/action/replication_record"}},"created_at":"2026-06-01T02:03:26.254101+00:00","updated_at":"2026-06-01T02:03:26.254101+00:00"}