{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2ZFIZHTXSZPMER3WU6TRDXQJJY","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":"74c5d833930e7783eb0348813e87570b8f91a01409266e8d41d59025bddfe245","cross_cats_sorted":["cs.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T10:50:35Z","title_canon_sha256":"acbb506a54e15c829b9a552ec97845892a0a3139816543199ae5832402daea19"},"schema_version":"1.0","source":{"id":"2503.16028","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16028","created_at":"2026-08-11T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16028v5","created_at":"2026-08-11T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16028","created_at":"2026-08-11T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"2ZFIZHTXSZPM","created_at":"2026-08-11T02:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"2ZFIZHTXSZPMER3W","created_at":"2026-08-11T02:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"2ZFIZHTX","created_at":"2026-08-11T02:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:ea545a31ff822b60f77f6a0e86dd3416009884c06688c4bd1258d5b143414e72","target":"graph","created_at":"2026-08-11T02:18:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.16028/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are defined on an infinite-dimensional function space, and the PDEs induce a computationally intensive likelihood function. Additionally, sparse data tends to lead to a multi-modal posterior. These features make it difficult to apply existing sequential Monte Carlo (SMC) algorithms. To overcome these difficulties, we propose new conditions for the likelihood fu","authors_text":"Deyu Meng, Haoyu Lu, Junxiong Jia","cross_cats":["cs.NA","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T10:50:35Z","title":"Sequential Monte Carlo with Gaussian Mixture Approximation for Infinite-Dimensional Statistical Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16028","kind":"arxiv","version":5},"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":"sha256:61d04f87e84b6070c674d28b9af169fcf035a5fcdf7c9ac60cc64a3c8537047b","target":"record","created_at":"2026-08-11T02:18:13Z","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":"74c5d833930e7783eb0348813e87570b8f91a01409266e8d41d59025bddfe245","cross_cats_sorted":["cs.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T10:50:35Z","title_canon_sha256":"acbb506a54e15c829b9a552ec97845892a0a3139816543199ae5832402daea19"},"schema_version":"1.0","source":{"id":"2503.16028","kind":"arxiv","version":5}},"canonical_sha256":"d64a8c9e77965ec24776a7a711de094e018b6fe9a7b8a512f2daade1dcc4ad50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d64a8c9e77965ec24776a7a711de094e018b6fe9a7b8a512f2daade1dcc4ad50","first_computed_at":"2026-08-11T02:18:13.060983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:18:13.060983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TJem51uMZ198zC5cyw0DU2xOwaX+bJACSUbRLujSc8x0w0COT9haeTA4e/1n7/GVTFID2kdEUJ+hZzTBUeGbAw==","signature_status":"signed_v1","signed_at":"2026-08-11T02:18:13.062836Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.16028","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61d04f87e84b6070c674d28b9af169fcf035a5fcdf7c9ac60cc64a3c8537047b","sha256:ea545a31ff822b60f77f6a0e86dd3416009884c06688c4bd1258d5b143414e72"],"state_sha256":"085076f1c02cb9a4408028f157d2d98b757e257396228e290cb9c395a8bc3e56"}