{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MMHLTM7JKCGS26AOLLQWJIWFZN","short_pith_number":"pith:MMHLTM7J","schema_version":"1.0","canonical_sha256":"630eb9b3e9508d2d780e5ae164a2c5cb6cfd5a20bd92fdef94792b28f9a9051d","source":{"kind":"arxiv","id":"1401.0654","version":1},"attestation_state":"computed","paper":{"title":"Numerical algorithms for the forward and backward fractional Feynman-Kac equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Eli Barkai, Minghua Chen, Weihua Deng","submitted_at":"2014-01-03T14:29:29Z","abstract_excerpt":"The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schr\\\"{o}dinger equation in imaginary time. The functionals of no-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac equation [J. Stat. Phys. 141, 1071-1092, 2010], where the fractional substantial derivative is involved. Based on recently developed discretized schemes for fractional substantial derivatives [arXiv:1310.3086], this pa"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.0654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-01-03T14:29:29Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"09eb27773968fcbda128e6677c61e96bf4f08bb2d547bc792e42cd3fb3fb5560","abstract_canon_sha256":"a5b06b022a2c8375f9cef31bc35d61743e13b13fd519b286a5a91dc28915ebee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:13.438622Z","signature_b64":"V+2OvFynx/qhKuAkMg1OlVkSWlkOxx7JZMmtpU3K9AuiY6MPOspnrJ+nfEwIbDVuEV5nBMmGwHJHz5RJqh8iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"630eb9b3e9508d2d780e5ae164a2c5cb6cfd5a20bd92fdef94792b28f9a9051d","last_reissued_at":"2026-05-18T02:28:13.437953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:13.437953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical algorithms for the forward and backward fractional Feynman-Kac equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Eli Barkai, Minghua Chen, Weihua Deng","submitted_at":"2014-01-03T14:29:29Z","abstract_excerpt":"The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schr\\\"{o}dinger equation in imaginary time. The functionals of no-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac equation [J. Stat. Phys. 141, 1071-1092, 2010], where the fractional substantial derivative is involved. Based on recently developed discretized schemes for fractional substantial derivatives [arXiv:1310.3086], this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0654","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.0654","created_at":"2026-05-18T02:28:13.438051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0654v1","created_at":"2026-05-18T02:28:13.438051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0654","created_at":"2026-05-18T02:28:13.438051+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMHLTM7JKCGS","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMHLTM7JKCGS26AO","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMHLTM7J","created_at":"2026-05-18T12:28:38.356838+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN","json":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN.json","graph_json":"https://pith.science/api/pith-number/MMHLTM7JKCGS26AOLLQWJIWFZN/graph.json","events_json":"https://pith.science/api/pith-number/MMHLTM7JKCGS26AOLLQWJIWFZN/events.json","paper":"https://pith.science/paper/MMHLTM7J"},"agent_actions":{"view_html":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN","download_json":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN.json","view_paper":"https://pith.science/paper/MMHLTM7J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0654&json=true","fetch_graph":"https://pith.science/api/pith-number/MMHLTM7JKCGS26AOLLQWJIWFZN/graph.json","fetch_events":"https://pith.science/api/pith-number/MMHLTM7JKCGS26AOLLQWJIWFZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN/action/storage_attestation","attest_author":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN/action/author_attestation","sign_citation":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN/action/citation_signature","submit_replication":"https://pith.science/pith/MMHLTM7JKCGS26AOLLQWJIWFZN/action/replication_record"}},"created_at":"2026-05-18T02:28:13.438051+00:00","updated_at":"2026-05-18T02:28:13.438051+00:00"}