{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FNVPWL7JMKG6YPVH42KP7NJIPI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"72838b15a4a6c76e3e74ee791acd95294962eefd963464b2a08dc0457ce2671a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T20:45:55Z","title_canon_sha256":"2039e2f36a2b9601550dbcd967f44773f28847d6f2213198a665b68a6a9a2cb4"},"schema_version":"1.0","source":{"id":"1810.03692","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03692","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03692v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03692","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"FNVPWL7JMKG6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FNVPWL7JMKG6YPVH","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FNVPWL7J","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:8cc299e1257ab0ee93a792db5990d575766aea513b740e68090069e18788b614","target":"graph","created_at":"2026-05-18T00:03:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\\in (0,1)$. The drift term is assumed to be globally Lipschitz. We prove that the solution of each of the above equations is continuous in terms of the index $H$, with respect to the convergence in law in the space of continuous functions.","authors_text":"Llu\\'is Quer-Sardanyons, Luca M. Giordano, Maria Jolis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T20:45:55Z","title":"SPDEs with fractional noise in space: continuity in law with respect to the Hurst index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03692","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:82366d519ccd9ba8621f6c4c99c19fe149303f08f141730ab45b3055b1d9496f","target":"record","created_at":"2026-05-18T00:03:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"72838b15a4a6c76e3e74ee791acd95294962eefd963464b2a08dc0457ce2671a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T20:45:55Z","title_canon_sha256":"2039e2f36a2b9601550dbcd967f44773f28847d6f2213198a665b68a6a9a2cb4"},"schema_version":"1.0","source":{"id":"1810.03692","kind":"arxiv","version":1}},"canonical_sha256":"2b6afb2fe9628dec3ea7e694ffb5287a2b0d3605951857db76db56c8bca8802c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b6afb2fe9628dec3ea7e694ffb5287a2b0d3605951857db76db56c8bca8802c","first_computed_at":"2026-05-18T00:03:44.744193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:44.744193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LAjVRAXfpShGGrmWQUkZG4NU1/odMXTIfe5AXaDR6S2HVrwPBPU/xNHkenQoU/J8fEI2RDHu/YoT1gnjWkjaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:44.744618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03692","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82366d519ccd9ba8621f6c4c99c19fe149303f08f141730ab45b3055b1d9496f","sha256:8cc299e1257ab0ee93a792db5990d575766aea513b740e68090069e18788b614"],"state_sha256":"6345e609e2ee6997486191528e5ba388742325b86a63a18c6896b79e3cd76087"}