{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5A4YNU5XUZGJHYU54HWJTIKMBJ","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":"48780df675a6cd39385b99330ff5ee28632edcb850cebf2f2e943aaf02045724","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-26T04:36:45Z","title_canon_sha256":"99cb016445080c7eb811734af558286e8c7089f0da54f631df5a249d17af7244"},"schema_version":"1.0","source":{"id":"1409.7468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7468","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7468v1","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7468","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"5A4YNU5XUZGJ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5A4YNU5XUZGJHYU5","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5A4YNU5X","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d6bce359c2dbe327f54608bb5497e3a1dd6975ab1151e56843a086cb5afa4948","target":"graph","created_at":"2026-05-18T00:56:38Z","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 time fractional stochastic heat type equation $$\\partial^\\beta_tu(t,x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\sigma(u)\\stackrel{\\cdot}{W}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0$, $\\beta\\in (0,1)$, $\\alpha\\in (0,2]$, $d<\\min\\{2,\\beta^{-1}\\}\\a$, $\\partial^\\beta_t$ is the Caputo fractional derivative, $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process, $\\stackrel{\\cdot}{W}(t,x)$ is space-time white noise, and $\\sigma:\\RR{R}\\to\\RR{R}$ is Lipschitz continuous.\n  The time fractional stochastic heat type equations might be used to model phenomenon with r","authors_text":"Erkan Nane, Jebessa B. Mijena","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-26T04:36:45Z","title":"Intermittence and time fractional stochastic partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7468","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:cabe699ac7d824fcc8c9ab8e070eb85571a087bfd089adb1a57c068867d439b2","target":"record","created_at":"2026-05-18T00:56:38Z","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":"48780df675a6cd39385b99330ff5ee28632edcb850cebf2f2e943aaf02045724","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-26T04:36:45Z","title_canon_sha256":"99cb016445080c7eb811734af558286e8c7089f0da54f631df5a249d17af7244"},"schema_version":"1.0","source":{"id":"1409.7468","kind":"arxiv","version":1}},"canonical_sha256":"e83986d3b7a64c93e29de1ec99a14c0a7a210dbfa88795a6c740bc8d3f91fecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e83986d3b7a64c93e29de1ec99a14c0a7a210dbfa88795a6c740bc8d3f91fecd","first_computed_at":"2026-05-18T00:56:38.336959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:38.336959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bUsQMcCKRDObu8/OyDC4ibb0aXe4jnMZHc2CWmKOV/ROLmubtTcnH+Qlbq5UY2n9LjG74SaLjm2g2SrazmSTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:38.337551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cabe699ac7d824fcc8c9ab8e070eb85571a087bfd089adb1a57c068867d439b2","sha256:d6bce359c2dbe327f54608bb5497e3a1dd6975ab1151e56843a086cb5afa4948"],"state_sha256":"5922fe798c8c140b00829b98feae9040d1520cd5248e7417f294a06ba2d10a65"}