{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E6XGANEEDRUYLWGCQVLWI53IFA","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":"54fa463be4a628df03365123c74f2d9d2765cbb5e6b0046167fa38c2c75d22b4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-04T15:48:18Z","title_canon_sha256":"1d364b06d3ac028b5ae1803d251e29b7ff78232c6211b4ed413bd5d6c8c0e9d7"},"schema_version":"1.0","source":{"id":"1605.01323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01323","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01323v2","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01323","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"E6XGANEEDRUY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6XGANEEDRUYLWGC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6XGANEE","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:efd3097aa98688357ea7527f44c3d3af8cf3afa43f648482b904d713bafa6db2","target":"graph","created_at":"2026-05-18T00:33:23Z","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":"Consider the following stochastic partial differential equation, \\begin{equation*} \\partial_t u_t(x)=\n  \\mathcal{L}u_t(x)+ \\xi\\sigma (u_t(x)) \\dot F(t,x), \\end{equation*} where $\\xi$ is a positive parameter and $\\sigma$ is a globally Lipschitz continuous function. The stochastic forcing term $\\dot F(t,x)$ is white in time but possibly colored in space. The operator $\\mathcal{L}$ is a non-local operator. We study the behaviour of the solution with respect to the parameter $\\xi$, extending the results in \\cite{FoonNual} and \\cite{Bin}","authors_text":"Erkan Nane, Mohammud Foondun, Ngartelbaye Guerngar","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-04T15:48:18Z","title":"Some properties of non-linear fractional stochastic heat equations on bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01323","kind":"arxiv","version":2},"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":"sha256:4ff0258ed312258deba66c19bc1b560ba76eb27a4eafd80ce80a8e5ec1a90712","target":"record","created_at":"2026-05-18T00:33:23Z","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":"54fa463be4a628df03365123c74f2d9d2765cbb5e6b0046167fa38c2c75d22b4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-04T15:48:18Z","title_canon_sha256":"1d364b06d3ac028b5ae1803d251e29b7ff78232c6211b4ed413bd5d6c8c0e9d7"},"schema_version":"1.0","source":{"id":"1605.01323","kind":"arxiv","version":2}},"canonical_sha256":"27ae6034841c6985d8c28557647768280b711605df2fd9bdfa5c56a71127eec6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27ae6034841c6985d8c28557647768280b711605df2fd9bdfa5c56a71127eec6","first_computed_at":"2026-05-18T00:33:23.734308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:23.734308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8eZvDOpsaJZrNuMUqpCcR7T9iarv6tMTM9V1thOzzHqP3tqLduYZyP+DuSEZPwbgvWjwHcVamO/5QGrL40I6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:23.734993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff0258ed312258deba66c19bc1b560ba76eb27a4eafd80ce80a8e5ec1a90712","sha256:efd3097aa98688357ea7527f44c3d3af8cf3afa43f648482b904d713bafa6db2"],"state_sha256":"1544e8fe919dbcea31ace1c46eb585500cb197ecf4aba18cb7560e0e54880211"}