{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IRSTAAKAWKA55IEV4KY2WF3V4G","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":"a4e36b5282a68ca393dd6881f7e5248270e791ae9266b4b160ea4b4d306fe0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-27T17:13:01Z","title_canon_sha256":"d3c75dc84910eb4dc3349e0e1bdec02a883333814cab6c84b65a27acda40e84a"},"schema_version":"1.0","source":{"id":"1404.6791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6791","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6791v1","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6791","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"IRSTAAKAWKA5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IRSTAAKAWKA55IEV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IRSTAAKA","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:f9b12295c082d90c0850b82b772973a9c232a03fd76151a015b2b63a197be7a8","target":"graph","created_at":"2026-05-18T02:53:05Z","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":"We consider nonlinear parabolic stochastic equations of the form $\\partial_t u=\\sL u + \\lambda \\sigma(u)\\dot \\xi$ on the ball $B(0,\\,R)$, where $\\dot \\xi$ denotes some Gaussian noise and $\\sigma$ is Lipschitz continuous. Here $\\sL$ corresponds to an $\\alpha$-stable process killed upon exiting $B(0, R)$. We will consider two types of noise; space-time white noise and spatially correlated noise. Under a linear growth condition on $\\sigma$, we study growth properties of the second moment of the solutions.","authors_text":"Kuanhou Tian, Mohammud Foondun, Wei Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-27T17:13:01Z","title":"On some properties of a class of fractional stochastic heat equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6791","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:c5a2020ac6bc74b9f443cce03bf35c5e9ff588d39551d0583b5552e3c600f37d","target":"record","created_at":"2026-05-18T02:53:05Z","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":"a4e36b5282a68ca393dd6881f7e5248270e791ae9266b4b160ea4b4d306fe0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-27T17:13:01Z","title_canon_sha256":"d3c75dc84910eb4dc3349e0e1bdec02a883333814cab6c84b65a27acda40e84a"},"schema_version":"1.0","source":{"id":"1404.6791","kind":"arxiv","version":1}},"canonical_sha256":"4465300140b281dea095e2b1ab1775e19d8338bd6f1a7d2370801144a9336819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4465300140b281dea095e2b1ab1775e19d8338bd6f1a7d2370801144a9336819","first_computed_at":"2026-05-18T02:53:05.915899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:05.915899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aN922w76rjkunQqtKdREF7tIcplIGMsAGXl/UiowRQQCtS2Iem/Dtqh404AJUjxIBCwL4OHWqjj901+loK5xAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:05.916428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5a2020ac6bc74b9f443cce03bf35c5e9ff588d39551d0583b5552e3c600f37d","sha256:f9b12295c082d90c0850b82b772973a9c232a03fd76151a015b2b63a197be7a8"],"state_sha256":"86c88101c842d79f39bda91166ff3728614133c060917295135fee96cfd6b928"}