{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KDBBZ4HSSLCCOLRODFBPQLMJCF","short_pith_number":"pith:KDBBZ4HS","canonical_record":{"source":{"id":"1505.04615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T12:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"acacfc12fde62e67dd98a7a332646da9fa36956bc588dc4baf13d6252c804068","abstract_canon_sha256":"4f9cb4db770fdb09b9016a198188bf868b4fb1ebc9d1164979f4a1ffd91b1728"},"schema_version":"1.0"},"canonical_sha256":"50c21cf0f292c4272e2e1942f82d89116a54390e8d1775fe93863d44ba09d50e","source":{"kind":"arxiv","id":"1505.04615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04615","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04615v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04615","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"KDBBZ4HSSLCC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KDBBZ4HSSLCCOLRO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KDBBZ4HS","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KDBBZ4HSSLCCOLRODFBPQLMJCF","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T12:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"acacfc12fde62e67dd98a7a332646da9fa36956bc588dc4baf13d6252c804068","abstract_canon_sha256":"4f9cb4db770fdb09b9016a198188bf868b4fb1ebc9d1164979f4a1ffd91b1728"},"schema_version":"1.0"},"canonical_sha256":"50c21cf0f292c4272e2e1942f82d89116a54390e8d1775fe93863d44ba09d50e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:25.009994Z","signature_b64":"TtXnjeU3//tbjwR6/2IV7Uqqb9Ny3CXXkkZh53uxwZqTTJzzNaNVTUHQN1ZXTA6AcMaoT17IHjnccqgOS9ZwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50c21cf0f292c4272e2e1942f82d89116a54390e8d1775fe93863d44ba09d50e","last_reissued_at":"2026-05-18T02:07:25.009563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:25.009563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04615","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p72P/qk9crQNnX5BgudzwiWeEZiW9Z0nxZkLGwKRNjxSDbIN2rkpXlHlB3tK1YexkhmsbzObiFAe8AW0OmTLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:44:30.311672Z"},"content_sha256":"9bd55523de6f952cebdf5a7e4d0bdfabe176b593d413aa93ea057b0c97b5f6af","schema_version":"1.0","event_id":"sha256:9bd55523de6f952cebdf5a7e4d0bdfabe176b593d413aa93ea057b0c97b5f6af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KDBBZ4HSSLCCOLRODFBPQLMJCF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic properties of some space-time fractional stochastic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mohammud Foondun","submitted_at":"2015-05-18T12:47:28Z","abstract_excerpt":"Consider non-linear time-fractional stochastic heat type equations of the following type, $$\\partial^\\beta_tu_t(x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\lambda \\sigma(u)\\stackrel{\\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$. The operator $\\partial^\\beta_t$ is the Caputo fractional derivative while $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process and $I^{1-\\beta}_t$ is the fractional integral operator. The forcing noise denoted by $\\stackrel{\\cdot}{F}(t,x)$ is a Gaussian noise. And the multiplicative non-linearity $\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04615","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFCwVUjAxHRss5mOXlemPUU42knBrigg5b9cl+GWyYzs7/ngYQNmA5JwhR4KW5wMUwwKMqlam0Wp6sXTJ3VzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:44:30.312373Z"},"content_sha256":"776ad1bf0b611cc4ce048f9d5dc7a7bd7f0c8dee9d83cba8930cb40c35189fac","schema_version":"1.0","event_id":"sha256:776ad1bf0b611cc4ce048f9d5dc7a7bd7f0c8dee9d83cba8930cb40c35189fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/bundle.json","state_url":"https://pith.science/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T11:44:30Z","links":{"resolver":"https://pith.science/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF","bundle":"https://pith.science/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/bundle.json","state":"https://pith.science/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDBBZ4HSSLCCOLRODFBPQLMJCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KDBBZ4HSSLCCOLRODFBPQLMJCF","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":"4f9cb4db770fdb09b9016a198188bf868b4fb1ebc9d1164979f4a1ffd91b1728","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T12:47:28Z","title_canon_sha256":"acacfc12fde62e67dd98a7a332646da9fa36956bc588dc4baf13d6252c804068"},"schema_version":"1.0","source":{"id":"1505.04615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04615","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04615v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04615","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"KDBBZ4HSSLCC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KDBBZ4HSSLCCOLRO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KDBBZ4HS","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:776ad1bf0b611cc4ce048f9d5dc7a7bd7f0c8dee9d83cba8930cb40c35189fac","target":"graph","created_at":"2026-05-18T02:07:25Z","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 non-linear time-fractional stochastic heat type equations of the following type, $$\\partial^\\beta_tu_t(x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\lambda \\sigma(u)\\stackrel{\\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$. The operator $\\partial^\\beta_t$ is the Caputo fractional derivative while $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process and $I^{1-\\beta}_t$ is the fractional integral operator. The forcing noise denoted by $\\stackrel{\\cdot}{F}(t,x)$ is a Gaussian noise. And the multiplicative non-linearity $\\s","authors_text":"Erkan Nane, Mohammud Foondun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T12:47:28Z","title":"Asymptotic properties of some space-time fractional stochastic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04615","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":"sha256:9bd55523de6f952cebdf5a7e4d0bdfabe176b593d413aa93ea057b0c97b5f6af","target":"record","created_at":"2026-05-18T02:07:25Z","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":"4f9cb4db770fdb09b9016a198188bf868b4fb1ebc9d1164979f4a1ffd91b1728","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T12:47:28Z","title_canon_sha256":"acacfc12fde62e67dd98a7a332646da9fa36956bc588dc4baf13d6252c804068"},"schema_version":"1.0","source":{"id":"1505.04615","kind":"arxiv","version":1}},"canonical_sha256":"50c21cf0f292c4272e2e1942f82d89116a54390e8d1775fe93863d44ba09d50e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50c21cf0f292c4272e2e1942f82d89116a54390e8d1775fe93863d44ba09d50e","first_computed_at":"2026-05-18T02:07:25.009563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:25.009563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TtXnjeU3//tbjwR6/2IV7Uqqb9Ny3CXXkkZh53uxwZqTTJzzNaNVTUHQN1ZXTA6AcMaoT17IHjnccqgOS9ZwBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:25.009994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bd55523de6f952cebdf5a7e4d0bdfabe176b593d413aa93ea057b0c97b5f6af","sha256:776ad1bf0b611cc4ce048f9d5dc7a7bd7f0c8dee9d83cba8930cb40c35189fac"],"state_sha256":"051b7735111b5bd88d60c1860b0f49316587a54ccdf58dfb58750345638ab203"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1diRCf/lhQuPjT1QKPRQ2J3XKlrGWvQ9FdUo3FJgPmq6hgRl7YeNIJQZyFwPcLYwrgPawMkXq684eV6K7o7wAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:44:30.316023Z","bundle_sha256":"e9565fce5ee47ffca8504c256b84d772a9447782c4baafaf119b29e3e1d96723"}}