{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:46WCWXSCK62QGMW4IKGESJNPGZ","short_pith_number":"pith:46WCWXSC","canonical_record":{"source":{"id":"1709.05585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-17T00:24:40Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e62d07911d7eaed6c89f21107f5d4192f37355be4c94c187d87516c0065f1530","abstract_canon_sha256":"b9c948642320a4efd4e15325c821c2bb969ffb20ecf66db3c05f861a423eeb0d"},"schema_version":"1.0"},"canonical_sha256":"e7ac2b5e4257b50332dc428c4925af365f3313799d1615dc37be0aa609bb23b8","source":{"kind":"arxiv","id":"1709.05585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05585","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05585v1","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05585","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"46WCWXSCK62Q","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"46WCWXSCK62QGMW4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"46WCWXSC","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:46WCWXSCK62QGMW4IKGESJNPGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-17T00:24:40Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e62d07911d7eaed6c89f21107f5d4192f37355be4c94c187d87516c0065f1530","abstract_canon_sha256":"b9c948642320a4efd4e15325c821c2bb969ffb20ecf66db3c05f861a423eeb0d"},"schema_version":"1.0"},"canonical_sha256":"e7ac2b5e4257b50332dc428c4925af365f3313799d1615dc37be0aa609bb23b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:00.241950Z","signature_b64":"hA/PQ3WxxPE/UMJBPpP1biI4P6qsMDMcOp40qa5y7X7qJk4XKshUlw2+sVrNYYZp/Fek3YpOP2iEfkSWNwAdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ac2b5e4257b50332dc428c4925af365f3313799d1615dc37be0aa609bb23b8","last_reissued_at":"2026-05-18T00:35:00.241202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:00.241202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05585","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":"2026-05-18T00:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2j/eIcwapOZmXmy5Nm7/dzEuajtWbi/r+URQAuEkXjPNeTcDEKzdsY3fESGo2xOIRI7/wi9HahGG674wbiJHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:04:16.480189Z"},"content_sha256":"0054198fd73eb77915ffa23d3181cbcc8b40516353535f9021b92e55142bc59a","schema_version":"1.0","event_id":"sha256:0054198fd73eb77915ffa23d3181cbcc8b40516353535f9021b92e55142bc59a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:46WCWXSCK62QGMW4IKGESJNPGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker-Planck Equations in Large Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andrew J. Majda, Nan Chen, Xin T. Tong","submitted_at":"2017-09-17T00:24:40Z","abstract_excerpt":"This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. Despite the conditional Gaussianity, these nonlinear systems contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy that requires only a small number of samples $L$ to capture both the transient and the equilibrium non-Gaussian PDFs with high accuracy. Here,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05585","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":"2026-05-18T00:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmfWPTtIfAmlUf0pXu0BuBw+23yUxS5Ty0RzKqOB7vwsE1cLBkYNeFs9LsodSSVn+BGTqTtkIe40ssF7PFkvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:04:16.480894Z"},"content_sha256":"709d316a15afd73473aa0bae2588c7b864522efbd380b1febc1e548ade9d9a7c","schema_version":"1.0","event_id":"sha256:709d316a15afd73473aa0bae2588c7b864522efbd380b1febc1e548ade9d9a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46WCWXSCK62QGMW4IKGESJNPGZ/bundle.json","state_url":"https://pith.science/pith/46WCWXSCK62QGMW4IKGESJNPGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46WCWXSCK62QGMW4IKGESJNPGZ/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":"2026-06-06T16:04:16Z","links":{"resolver":"https://pith.science/pith/46WCWXSCK62QGMW4IKGESJNPGZ","bundle":"https://pith.science/pith/46WCWXSCK62QGMW4IKGESJNPGZ/bundle.json","state":"https://pith.science/pith/46WCWXSCK62QGMW4IKGESJNPGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46WCWXSCK62QGMW4IKGESJNPGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:46WCWXSCK62QGMW4IKGESJNPGZ","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":"b9c948642320a4efd4e15325c821c2bb969ffb20ecf66db3c05f861a423eeb0d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-17T00:24:40Z","title_canon_sha256":"e62d07911d7eaed6c89f21107f5d4192f37355be4c94c187d87516c0065f1530"},"schema_version":"1.0","source":{"id":"1709.05585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05585","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05585v1","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05585","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"46WCWXSCK62Q","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"46WCWXSCK62QGMW4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"46WCWXSC","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:709d316a15afd73473aa0bae2588c7b864522efbd380b1febc1e548ade9d9a7c","target":"graph","created_at":"2026-05-18T00:35:00Z","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":"This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. Despite the conditional Gaussianity, these nonlinear systems contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy that requires only a small number of samples $L$ to capture both the transient and the equilibrium non-Gaussian PDFs with high accuracy. Here,","authors_text":"Andrew J. Majda, Nan Chen, Xin T. Tong","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-17T00:24:40Z","title":"Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker-Planck Equations in Large Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05585","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":"sha256:0054198fd73eb77915ffa23d3181cbcc8b40516353535f9021b92e55142bc59a","target":"record","created_at":"2026-05-18T00:35:00Z","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":"b9c948642320a4efd4e15325c821c2bb969ffb20ecf66db3c05f861a423eeb0d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-17T00:24:40Z","title_canon_sha256":"e62d07911d7eaed6c89f21107f5d4192f37355be4c94c187d87516c0065f1530"},"schema_version":"1.0","source":{"id":"1709.05585","kind":"arxiv","version":1}},"canonical_sha256":"e7ac2b5e4257b50332dc428c4925af365f3313799d1615dc37be0aa609bb23b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ac2b5e4257b50332dc428c4925af365f3313799d1615dc37be0aa609bb23b8","first_computed_at":"2026-05-18T00:35:00.241202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:00.241202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hA/PQ3WxxPE/UMJBPpP1biI4P6qsMDMcOp40qa5y7X7qJk4XKshUlw2+sVrNYYZp/Fek3YpOP2iEfkSWNwAdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:00.241950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0054198fd73eb77915ffa23d3181cbcc8b40516353535f9021b92e55142bc59a","sha256:709d316a15afd73473aa0bae2588c7b864522efbd380b1febc1e548ade9d9a7c"],"state_sha256":"10269e21d23bf8598a82100e45a0a072a6b4460a2e0665b658e84d576f79b274"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9s+OUaTaEHCQ8xR3EfEVwec9hXPtRhT+Wy8XjUpHN+wlbRJO13FKNOczAhvqCn24O3paxnsLVh/KZRvzLbwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:04:16.483718Z","bundle_sha256":"6253cb0db10168b94ab7eb800bd315f8ac14f4947f2c2d83086c8b0187c0934e"}}