{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YDITW4IIIBW7P5KHZPHC6PHOB7","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":"d13cac02f9e6d59beb40bb30d86eac8914836931e0851acd012dd9cb7ee19768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-07T13:51:07Z","title_canon_sha256":"11e3d8e4e31ef5dc01507458c8c63a8d377569d0179bdee022716945ba148589"},"schema_version":"1.0","source":{"id":"1810.03144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03144","created_at":"2026-05-18T00:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03144v1","created_at":"2026-05-18T00:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03144","created_at":"2026-05-18T00:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"YDITW4IIIBW7","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YDITW4IIIBW7P5KH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YDITW4II","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:e7d3d5f80b0c189da18dd23b67d2ca10d4b09aadb65b2e99cbb61cd52c63034f","target":"graph","created_at":"2026-05-18T00:03:54Z","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":"In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\\partial_t^\\alpha u(x,t)+\\mathcal{A} u(x,t)=f(x)h(t)+g(x) \\dot{\\mathbb{W}}(t).$$ The interested inverse problem is to reconstruct $f(x)$ and $g(x)$ by the statistics of the final time data $u(x,T).$ Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then the reconstruction scheme for $f$ and $g$ is given. To tackle the ill-posedness, the Tikhonov regularization is adopted. Finally we give a regula","authors_text":"Pingping Niu, Tapio Helin, Zhidong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-07T13:51:07Z","title":"An inverse random source problem in a stochastic fractional diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03144","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":"sha256:014a34c41f7abf44a1f2caaca8ef524db5232b89c4aa37d57dad8c39a74c0bef","target":"record","created_at":"2026-05-18T00:03:54Z","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":"d13cac02f9e6d59beb40bb30d86eac8914836931e0851acd012dd9cb7ee19768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-07T13:51:07Z","title_canon_sha256":"11e3d8e4e31ef5dc01507458c8c63a8d377569d0179bdee022716945ba148589"},"schema_version":"1.0","source":{"id":"1810.03144","kind":"arxiv","version":1}},"canonical_sha256":"c0d13b7108406df7f547cbce2f3cee0ffdfef1e70022855da31111192db9f4ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0d13b7108406df7f547cbce2f3cee0ffdfef1e70022855da31111192db9f4ce","first_computed_at":"2026-05-18T00:03:54.390115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:54.390115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6iplbKOIsxbZBk5/c3cIZPEtYn39S3XSIsd9PaoBqgyAQVR3tq0YfASMCiP/clYpAQpSnp0Jo8iJ03BR31TDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:54.390758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:014a34c41f7abf44a1f2caaca8ef524db5232b89c4aa37d57dad8c39a74c0bef","sha256:e7d3d5f80b0c189da18dd23b67d2ca10d4b09aadb65b2e99cbb61cd52c63034f"],"state_sha256":"c689b7379dc963e959f3427607f1ee2ba10d2d35c31e7e25f2a8298b7b63040f"}