{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IX4KLKEA3PZZQXPE77Z3DWHQRX","short_pith_number":"pith:IX4KLKEA","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"},"canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","source":{"kind":"arxiv","id":"1703.09359","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IX4KLKEA3PZZQXPE77Z3DWHQRX","target":"record","payload":{"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"},"canonical_sha256":"45f8a5a880dbf3985de4fff3b1d8f08ddc8596fcebffa254ec9a481b9c23f442","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"},"source_kind":"arxiv","source_id":"1703.09359","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDxU4Su05kO/K36nOiQXncQKb+hVvO+aiNDg+S/oP2KaQNSbPkOfHUcknBJj9rW85H9lkcNrlBTqykFBCSNXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:44:44.527376Z"},"content_sha256":"479f8074e6049b942651a0e0b6261327b38efb6fbc3f91b484ef157568ec425c","schema_version":"1.0","event_id":"sha256:479f8074e6049b942651a0e0b6261327b38efb6fbc3f91b484ef157568ec425c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IX4KLKEA3PZZQXPE77Z3DWHQRX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFgewQgtin68WHiROjNqSAz9WYlna6IFCqfAEQ6vuHiiJ8jDVPeLfzZHy6cofj4Xe+ApqPMjPlRoOM82RjqgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:44:44.528101Z"},"content_sha256":"0568230b00eedf289e51ca24708d7af3d5b602960ef6d382677ea0536cee4e41","schema_version":"1.0","event_id":"sha256:0568230b00eedf289e51ca24708d7af3d5b602960ef6d382677ea0536cee4e41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/bundle.json","state_url":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T23:44:44Z","links":{"resolver":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX","bundle":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/bundle.json","state":"https://pith.science/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IX4KLKEA3PZZQXPE77Z3DWHQRX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMflxWHevSrrSwObd6cl2htWU62SvStf6iAXk+QkvE1VwLBPOtc/Pbu5YJNhMhcLMV7b49G3OO7bUC4GDsLrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:44:44.531740Z","bundle_sha256":"ba81bae232d41b612187dea71399fce4bff6b6829d1ffa595130d0943be22fcb"}}