{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GE4TVN5UO7BWW44WSJY7SBCABQ","short_pith_number":"pith:GE4TVN5U","schema_version":"1.0","canonical_sha256":"31393ab7b477c36b73969271f904400c128e85b5f9e908eaf5341545b27f8859","source":{"kind":"arxiv","id":"1602.07262","version":1},"attestation_state":"computed","paper":{"title":"Intermittency fronts for space-time fractional stochastic partial differential equations in $(d+1)$ dimensions","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, Sunday A. Asogwa","submitted_at":"2016-02-23T18:45:59Z","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 $\\sigma:\\R \\to\\RR{R}$ is Lipschitz continuous. Mijena and Nane proved in \\cite{JebesaAndNane1} that : (i) absolute moments of the solutions of "},"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":"1602.07262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T18:45:59Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"b20dacb102adbe0baadc4869846fa6b98ff6f16e8056b43ec80a7d885ea5cd85","abstract_canon_sha256":"cd598701f8792b36830ad235f2262afc6e9b84ff4c52571cb34116c30b092600"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:06.814076Z","signature_b64":"6HGfoDF5SjXO+0xKBVanO7RMrfKuT/hk4z71Cv4eu6/+nu3+x+25y4hGVK4PpaFtaFBWb4rcv3LDsOAx2cWcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31393ab7b477c36b73969271f904400c128e85b5f9e908eaf5341545b27f8859","last_reissued_at":"2026-05-18T01:20:06.813378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:06.813378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intermittency fronts for space-time fractional stochastic partial differential equations in $(d+1)$ dimensions","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, Sunday A. Asogwa","submitted_at":"2016-02-23T18:45:59Z","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 $\\sigma:\\R \\to\\RR{R}$ is Lipschitz continuous. Mijena and Nane proved in \\cite{JebesaAndNane1} that : (i) absolute moments of the solutions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07262","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":"1602.07262","created_at":"2026-05-18T01:20:06.813485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.07262v1","created_at":"2026-05-18T01:20:06.813485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07262","created_at":"2026-05-18T01:20:06.813485+00:00"},{"alias_kind":"pith_short_12","alias_value":"GE4TVN5UO7BW","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GE4TVN5UO7BWW44W","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GE4TVN5U","created_at":"2026-05-18T12:30:19.053100+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/GE4TVN5UO7BWW44WSJY7SBCABQ","json":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ.json","graph_json":"https://pith.science/api/pith-number/GE4TVN5UO7BWW44WSJY7SBCABQ/graph.json","events_json":"https://pith.science/api/pith-number/GE4TVN5UO7BWW44WSJY7SBCABQ/events.json","paper":"https://pith.science/paper/GE4TVN5U"},"agent_actions":{"view_html":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ","download_json":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ.json","view_paper":"https://pith.science/paper/GE4TVN5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.07262&json=true","fetch_graph":"https://pith.science/api/pith-number/GE4TVN5UO7BWW44WSJY7SBCABQ/graph.json","fetch_events":"https://pith.science/api/pith-number/GE4TVN5UO7BWW44WSJY7SBCABQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ/action/storage_attestation","attest_author":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ/action/author_attestation","sign_citation":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ/action/citation_signature","submit_replication":"https://pith.science/pith/GE4TVN5UO7BWW44WSJY7SBCABQ/action/replication_record"}},"created_at":"2026-05-18T01:20:06.813485+00:00","updated_at":"2026-05-18T01:20:06.813485+00:00"}