{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IX4KLKEA3PZZQXPE77Z3DWHQRX","short_pith_number":"pith:IX4KLKEA","schema_version":"1.0","canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","source":{"kind":"arxiv","id":"1703.09359","version":1},"attestation_state":"computed","paper":{"title":"Point cloud discretization of Fokker-Planck operators for committor functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Rongjie Lai","submitted_at":"2017-03-28T00:49:27Z","abstract_excerpt":"The committor functions provide useful information to the understanding of transitions of a stochastic system between disjoint regions in phase space. In this work, we develop a point cloud discretization for Fokker-Planck operators to numerically calculate the committor function, with the assumption that the transition occurs on an intrinsically low-dimensional manifold in the ambient potentially high dimensional configurational space of the stochastic system. Numerical examples on model systems validate the effectiveness of the proposed method."},"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":"1703.09359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-28T00:49:27Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"9c6befe5e3447fc01d641f5b2be5843638148ad4e9fc1c685f518e1a6900d0fa","abstract_canon_sha256":"a4a7c13f7920dfed1ccad20fb7579df3c5fd6f256260c9dad625f0a983b5fcef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:39.720596Z","signature_b64":"llMPRx4XJz3cG+oajWBEiMorUVflsCgHlGifSzDvBfrQVdjJgqCb07/JyIbu5A6lww2etG81M8XrbuQmmEtADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","last_reissued_at":"2026-05-18T00:47:39.719947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:39.719947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Point cloud discretization of Fokker-Planck operators for committor functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Rongjie Lai","submitted_at":"2017-03-28T00:49:27Z","abstract_excerpt":"The committor functions provide useful information to the understanding of transitions of a stochastic system between disjoint regions in phase space. In this work, we develop a point cloud discretization for Fokker-Planck operators to numerically calculate the committor function, with the assumption that the transition occurs on an intrinsically low-dimensional manifold in the ambient potentially high dimensional configurational space of the stochastic system. Numerical examples on model systems validate the effectiveness of the proposed method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09359","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":"1703.09359","created_at":"2026-05-18T00:47:39.720044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.09359v1","created_at":"2026-05-18T00:47:39.720044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09359","created_at":"2026-05-18T00:47:39.720044+00:00"},{"alias_kind":"pith_short_12","alias_value":"IX4KLKEA3PZZ","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IX4KLKEA3PZZQXPE","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IX4KLKEA","created_at":"2026-05-18T12:31:21.493067+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/IX4KLKEA3PZZQXPE77Z3DWHQRX","json":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX.json","graph_json":"https://pith.science/api/pith-number/IX4KLKEA3PZZQXPE77Z3DWHQRX/graph.json","events_json":"https://pith.science/api/pith-number/IX4KLKEA3PZZQXPE77Z3DWHQRX/events.json","paper":"https://pith.science/paper/IX4KLKEA"},"agent_actions":{"view_html":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX","download_json":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX.json","view_paper":"https://pith.science/paper/IX4KLKEA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.09359&json=true","fetch_graph":"https://pith.science/api/pith-number/IX4KLKEA3PZZQXPE77Z3DWHQRX/graph.json","fetch_events":"https://pith.science/api/pith-number/IX4KLKEA3PZZQXPE77Z3DWHQRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/action/storage_attestation","attest_author":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/action/author_attestation","sign_citation":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/action/citation_signature","submit_replication":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/action/replication_record"}},"created_at":"2026-05-18T00:47:39.720044+00:00","updated_at":"2026-05-18T00:47:39.720044+00:00"}