{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IX4KLKEA3PZZQXPE77Z3DWHQRX","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":"a4a7c13f7920dfed1ccad20fb7579df3c5fd6f256260c9dad625f0a983b5fcef","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-28T00:49:27Z","title_canon_sha256":"9c6befe5e3447fc01d641f5b2be5843638148ad4e9fc1c685f518e1a6900d0fa"},"schema_version":"1.0","source":{"id":"1703.09359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09359","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09359v1","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09359","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"IX4KLKEA3PZZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IX4KLKEA3PZZQXPE","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IX4KLKEA","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:0568230b00eedf289e51ca24708d7af3d5b602960ef6d382677ea0536cee4e41","target":"graph","created_at":"2026-05-18T00:47:39Z","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 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.","authors_text":"Jianfeng Lu, Rongjie Lai","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-28T00:49:27Z","title":"Point cloud discretization of Fokker-Planck operators for committor functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09359","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":"sha256:479f8074e6049b942651a0e0b6261327b38efb6fbc3f91b484ef157568ec425c","target":"record","created_at":"2026-05-18T00:47:39Z","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":"a4a7c13f7920dfed1ccad20fb7579df3c5fd6f256260c9dad625f0a983b5fcef","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-28T00:49:27Z","title_canon_sha256":"9c6befe5e3447fc01d641f5b2be5843638148ad4e9fc1c685f518e1a6900d0fa"},"schema_version":"1.0","source":{"id":"1703.09359","kind":"arxiv","version":1}},"canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","first_computed_at":"2026-05-18T00:47:39.719947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:39.719947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llMPRx4XJz3cG+oajWBEiMorUVflsCgHlGifSzDvBfrQVdjJgqCb07/JyIbu5A6lww2etG81M8XrbuQmmEtADw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:39.720596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:479f8074e6049b942651a0e0b6261327b38efb6fbc3f91b484ef157568ec425c","sha256:0568230b00eedf289e51ca24708d7af3d5b602960ef6d382677ea0536cee4e41"],"state_sha256":"e91816e8106b93beb75f1e4ed04100bf80bf1b0a9226f78c712b0e4fb8e1d862"}