{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7QQUT4OKDTMXMJJTFFW6HAKRWA","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":"c7c3b502db3b36d9a77cf50695ebf612e4a9f7f5f0a37fe1b558f00aee3f5b72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-11T02:40:05Z","title_canon_sha256":"95c7e82d4d57dc33381c4ceef48207e67f146dba39509744d9d160aaf6f317af"},"schema_version":"1.0","source":{"id":"1904.05501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05501","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05501v1","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05501","created_at":"2026-05-17T23:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"7QQUT4OKDTMX","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7QQUT4OKDTMXMJJT","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7QQUT4OK","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:74d9acc3012a2e9a61727d778f4513ad155df7283e57774f5b95de83e753fd15","target":"graph","created_at":"2026-05-17T23:48:44Z","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 chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\\alpha\\in(0,1)$. Our survey covers the following types of inverse problems: 1. determination of time-dependent functions in interior source terms 2. determination of space-dependent functions in interior source terms 3. determination of time-dependent functions appearing in boundary conditions","authors_text":"Masahiro Yamamoto, Yikan Liu, Zhiyuan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-11T02:40:05Z","title":"Inverse Problems of Determining Sources of the Fractional Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05501","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":"sha256:6160fe690a8b4907f57459e49b3056bad8a6c3b2556071b8aadddbbae88db2c0","target":"record","created_at":"2026-05-17T23:48:44Z","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":"c7c3b502db3b36d9a77cf50695ebf612e4a9f7f5f0a37fe1b558f00aee3f5b72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-11T02:40:05Z","title_canon_sha256":"95c7e82d4d57dc33381c4ceef48207e67f146dba39509744d9d160aaf6f317af"},"schema_version":"1.0","source":{"id":"1904.05501","kind":"arxiv","version":1}},"canonical_sha256":"fc2149f1ca1cd9762533296de38151b00ef9088a2eca3e38d0b2a08de09b26b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc2149f1ca1cd9762533296de38151b00ef9088a2eca3e38d0b2a08de09b26b1","first_computed_at":"2026-05-17T23:48:44.860139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:44.860139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsIdJq4EQLFqr4QzH5ISwrzqP+q12JsXkBxACsgZXg8Klt1xD6Elt/1VbFN9vndyn8K9DQ9ndYIan9GzGCWTBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:44.860593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6160fe690a8b4907f57459e49b3056bad8a6c3b2556071b8aadddbbae88db2c0","sha256:74d9acc3012a2e9a61727d778f4513ad155df7283e57774f5b95de83e753fd15"],"state_sha256":"3523aa3a288c7f31cc4f1d29acfa11d64c0e98834a5c3ba01d68bd5a9f351249"}