{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:T4W6JZFLTYEICVIA43CEDYCVLR","short_pith_number":"pith:T4W6JZFL","canonical_record":{"source":{"id":"1811.05391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-13T16:34:47Z","cross_cats_sorted":[],"title_canon_sha256":"8f6186bb80a9c90d112b08d08151e9adb57e683dc0b4e02647de6d051c1ad4de","abstract_canon_sha256":"fb51ce857140e0bcf59cb26ae5d5e3019a14f36b78b7cc4072b6663f744f6559"},"schema_version":"1.0"},"canonical_sha256":"9f2de4e4ab9e08815500e6c441e0555c4e7315e32bed69a20d10fff6ac3c59bd","source":{"kind":"arxiv","id":"1811.05391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05391","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05391v1","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05391","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"T4W6JZFLTYEI","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T4W6JZFLTYEICVIA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T4W6JZFL","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:T4W6JZFLTYEICVIA43CEDYCVLR","target":"record","payload":{"canonical_record":{"source":{"id":"1811.05391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-13T16:34:47Z","cross_cats_sorted":[],"title_canon_sha256":"8f6186bb80a9c90d112b08d08151e9adb57e683dc0b4e02647de6d051c1ad4de","abstract_canon_sha256":"fb51ce857140e0bcf59cb26ae5d5e3019a14f36b78b7cc4072b6663f744f6559"},"schema_version":"1.0"},"canonical_sha256":"9f2de4e4ab9e08815500e6c441e0555c4e7315e32bed69a20d10fff6ac3c59bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.260046Z","signature_b64":"JbCIpYcbJ+E9o7pAxky/rT4UDuw/KSJvTVhndvQivoNQPeMhG103XL7S9uTNEvbUlLpIAxMvyWpV5JR8cBbkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f2de4e4ab9e08815500e6c441e0555c4e7315e32bed69a20d10fff6ac3c59bd","last_reissued_at":"2026-05-18T00:00:46.259579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.259579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.05391","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":"2026-05-18T00:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKL9nDF6t3hmguLYsFZDbUbsconHADzzvDcfKeQ8tITvqLutlRVXlPBqK8VZU99tVJaR2ANjste23HEcOFLACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:51:14.762787Z"},"content_sha256":"3309618be92217e43fe03ee7031247439475d3d7bb65b6d3ab2f9f4b44a1036b","schema_version":"1.0","event_id":"sha256:3309618be92217e43fe03ee7031247439475d3d7bb65b6d3ab2f9f4b44a1036b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:T4W6JZFLTYEICVIA43CEDYCVLR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on a fractional-time stochastic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mohammud Foondun","submitted_at":"2018-11-13T16:34:47Z","abstract_excerpt":"We consider a class of fractional time stochastic equation defined on a bounded domain and show that the presence of the time derivative induces a significant change in the qualitative behaviour of the solutions. This is in sharp contrast with the phenomenon showcased in earlier works. We also show that as one {\\it tunes off the fractional} in the fractional time derivative, the solution behaves more and more like its {\\it usual} counterpart."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05391","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":"2026-05-18T00:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6/NbhAaHp/Krr6jd+aQ/QGTricoG8eKr+f/R44O5LWlIVPV1HmC8afThe9TIpX6F0nru45aEVrDHNl/YB8ygDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:51:14.763127Z"},"content_sha256":"d70fa7f6559f4f4d684a26a3f42c381740a0f5c038d55c6e8bb2877eadb02cfb","schema_version":"1.0","event_id":"sha256:d70fa7f6559f4f4d684a26a3f42c381740a0f5c038d55c6e8bb2877eadb02cfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4W6JZFLTYEICVIA43CEDYCVLR/bundle.json","state_url":"https://pith.science/pith/T4W6JZFLTYEICVIA43CEDYCVLR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4W6JZFLTYEICVIA43CEDYCVLR/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":"2026-05-26T11:51:14Z","links":{"resolver":"https://pith.science/pith/T4W6JZFLTYEICVIA43CEDYCVLR","bundle":"https://pith.science/pith/T4W6JZFLTYEICVIA43CEDYCVLR/bundle.json","state":"https://pith.science/pith/T4W6JZFLTYEICVIA43CEDYCVLR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4W6JZFLTYEICVIA43CEDYCVLR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T4W6JZFLTYEICVIA43CEDYCVLR","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":"fb51ce857140e0bcf59cb26ae5d5e3019a14f36b78b7cc4072b6663f744f6559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-13T16:34:47Z","title_canon_sha256":"8f6186bb80a9c90d112b08d08151e9adb57e683dc0b4e02647de6d051c1ad4de"},"schema_version":"1.0","source":{"id":"1811.05391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05391","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05391v1","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05391","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"T4W6JZFLTYEI","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T4W6JZFLTYEICVIA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T4W6JZFL","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:d70fa7f6559f4f4d684a26a3f42c381740a0f5c038d55c6e8bb2877eadb02cfb","target":"graph","created_at":"2026-05-18T00:00:46Z","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 a class of fractional time stochastic equation defined on a bounded domain and show that the presence of the time derivative induces a significant change in the qualitative behaviour of the solutions. This is in sharp contrast with the phenomenon showcased in earlier works. We also show that as one {\\it tunes off the fractional} in the fractional time derivative, the solution behaves more and more like its {\\it usual} counterpart.","authors_text":"Mohammud Foondun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-13T16:34:47Z","title":"Remarks on a fractional-time stochastic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05391","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":"sha256:3309618be92217e43fe03ee7031247439475d3d7bb65b6d3ab2f9f4b44a1036b","target":"record","created_at":"2026-05-18T00:00:46Z","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":"fb51ce857140e0bcf59cb26ae5d5e3019a14f36b78b7cc4072b6663f744f6559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-13T16:34:47Z","title_canon_sha256":"8f6186bb80a9c90d112b08d08151e9adb57e683dc0b4e02647de6d051c1ad4de"},"schema_version":"1.0","source":{"id":"1811.05391","kind":"arxiv","version":1}},"canonical_sha256":"9f2de4e4ab9e08815500e6c441e0555c4e7315e32bed69a20d10fff6ac3c59bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f2de4e4ab9e08815500e6c441e0555c4e7315e32bed69a20d10fff6ac3c59bd","first_computed_at":"2026-05-18T00:00:46.259579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:46.259579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JbCIpYcbJ+E9o7pAxky/rT4UDuw/KSJvTVhndvQivoNQPeMhG103XL7S9uTNEvbUlLpIAxMvyWpV5JR8cBbkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:46.260046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3309618be92217e43fe03ee7031247439475d3d7bb65b6d3ab2f9f4b44a1036b","sha256:d70fa7f6559f4f4d684a26a3f42c381740a0f5c038d55c6e8bb2877eadb02cfb"],"state_sha256":"22fd863f116fe843e816886857a32008fcbe595d1b020b1a4a1b2d755dad863a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/D0fJG+vgMK/Fh54XKY6iKWBp9enph6LnMLPLPGZjFoaD+XoepZl6Peu3F08nn/VgsmU1UKCrExERkjweeOBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:51:14.765271Z","bundle_sha256":"f37b362b37a065d4c67c1e03304db25ab2f49eaa9384ce9bb7f2cfb03e0957d4"}}