{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TBYHO5JMQVG4TUZ3L43YIUCGK4","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":"950f65caac6e4d3c1d9dadd3cb51582be88dfa11f82a1c94185903de79f1333c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-25T11:46:08Z","title_canon_sha256":"87b9140a3b1fe4e33fccf3f86e0b03b2a9e12f3fc01071e024f1d7a6cad93025"},"schema_version":"1.0","source":{"id":"1607.07221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07221","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07221v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07221","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"TBYHO5JMQVG4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TBYHO5JMQVG4TUZ3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TBYHO5JM","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:8ed2df1ea149da102db1d83865b7241d5cd5ca84f4ec7017e9d90f4e2345031a","target":"graph","created_at":"2026-05-18T01:10:34Z","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":"The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the discretized schemes for fractional substantial derivatives proposed recently, we construct compact finite difference schemes for the backward fractional Feynman-Kac equation, which has q-th (q=1, 2, 3, 4) order accuracy in temporal direction and fourth orde","authors_text":"Jiahui Hu, Jungang Wang, Yufeng Nie, Zhanbin Yuan, Zongze Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-25T11:46:08Z","title":"Maximum-norm error analysis of compact difference schemes for the backward fractional Feynman-Kac equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07221","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":"sha256:43ca7aafbc6c6fb03f023e16ac5e5136c83358e9162dc84c1f37cc77fa336970","target":"record","created_at":"2026-05-18T01:10:34Z","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":"950f65caac6e4d3c1d9dadd3cb51582be88dfa11f82a1c94185903de79f1333c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-25T11:46:08Z","title_canon_sha256":"87b9140a3b1fe4e33fccf3f86e0b03b2a9e12f3fc01071e024f1d7a6cad93025"},"schema_version":"1.0","source":{"id":"1607.07221","kind":"arxiv","version":1}},"canonical_sha256":"987077752c854dc9d33b5f37845046572dccff2d50eb3cb4c73e47c23c409de2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"987077752c854dc9d33b5f37845046572dccff2d50eb3cb4c73e47c23c409de2","first_computed_at":"2026-05-18T01:10:34.446044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:34.446044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/S+4rOPgeX3ZzSJ0G5uufwSfZtkmO7ylGAIiu2m357xXk9FwpNC+Njj5CAjboqvbvv3Y2t68HrUfBuRBXkFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:34.446621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43ca7aafbc6c6fb03f023e16ac5e5136c83358e9162dc84c1f37cc77fa336970","sha256:8ed2df1ea149da102db1d83865b7241d5cd5ca84f4ec7017e9d90f4e2345031a"],"state_sha256":"a6edcc59e0f722df0dbd8c5af2bfbcc968c148ede9a4cbe73aefce35d6e103f1"}