{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:O72GW5X6XC7AECU5VYE7OL7IOD","short_pith_number":"pith:O72GW5X6","schema_version":"1.0","canonical_sha256":"77f46b76feb8be020a9dae09f72fe870ffd39d4a74b18d9d4981ba1029c2af23","source":{"kind":"arxiv","id":"1409.7366","version":1},"attestation_state":"computed","paper":{"title":"Space-time fractional stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Jebessa B. Mijena","submitted_at":"2014-09-25T18:57:03Z","abstract_excerpt":"We consider non-linear 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 $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$ and $d<\\min\\{2,\\beta^{-1}\\}\\a$, $\\partial^\\beta_t$ is the Caputo fractional derivative, $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process, $I^{1-\\beta}_t$ is the fractional integral operator, $\\stackrel{\\cdot}{W}(t,x)$ is space-time white noise, and $\\sigma:\\RR{R}\\to\\RR{R}$ is Lipschitz continuous.\n  Time fractional stochastic"},"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":"1409.7366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-25T18:57:03Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"88f5a504c9ec3dfec82f37f910fca5cd61bee87dd22615f6354bb9a5c7f1a707","abstract_canon_sha256":"290e7d20c11b66d99f5324ff1905e1d9536b76ad1245d369f59b198da7ab18a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:38.348009Z","signature_b64":"YeUjuWcbezn2OPxqUHhIfpk0ZQgiMhTG9mkAQ9+7tYfP7sJo2/KWaqrsuZwfqcTvxz0nqsFZnkShsjG501DrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77f46b76feb8be020a9dae09f72fe870ffd39d4a74b18d9d4981ba1029c2af23","last_reissued_at":"2026-05-18T00:56:38.347299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:38.347299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space-time fractional stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Jebessa B. Mijena","submitted_at":"2014-09-25T18:57:03Z","abstract_excerpt":"We consider non-linear 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 $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$ and $d<\\min\\{2,\\beta^{-1}\\}\\a$, $\\partial^\\beta_t$ is the Caputo fractional derivative, $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process, $I^{1-\\beta}_t$ is the fractional integral operator, $\\stackrel{\\cdot}{W}(t,x)$ is space-time white noise, and $\\sigma:\\RR{R}\\to\\RR{R}$ is Lipschitz continuous.\n  Time fractional stochastic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7366","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1409.7366","created_at":"2026-05-18T00:56:38.347414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.7366v1","created_at":"2026-05-18T00:56:38.347414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7366","created_at":"2026-05-18T00:56:38.347414+00:00"},{"alias_kind":"pith_short_12","alias_value":"O72GW5X6XC7A","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"O72GW5X6XC7AECU5","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"O72GW5X6","created_at":"2026-05-18T12:28:41.024544+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/O72GW5X6XC7AECU5VYE7OL7IOD","json":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD.json","graph_json":"https://pith.science/api/pith-number/O72GW5X6XC7AECU5VYE7OL7IOD/graph.json","events_json":"https://pith.science/api/pith-number/O72GW5X6XC7AECU5VYE7OL7IOD/events.json","paper":"https://pith.science/paper/O72GW5X6"},"agent_actions":{"view_html":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD","download_json":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD.json","view_paper":"https://pith.science/paper/O72GW5X6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.7366&json=true","fetch_graph":"https://pith.science/api/pith-number/O72GW5X6XC7AECU5VYE7OL7IOD/graph.json","fetch_events":"https://pith.science/api/pith-number/O72GW5X6XC7AECU5VYE7OL7IOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD/action/storage_attestation","attest_author":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD/action/author_attestation","sign_citation":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD/action/citation_signature","submit_replication":"https://pith.science/pith/O72GW5X6XC7AECU5VYE7OL7IOD/action/replication_record"}},"created_at":"2026-05-18T00:56:38.347414+00:00","updated_at":"2026-05-18T00:56:38.347414+00:00"}