{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:5CSXLKYCGZEUUOXO37HS7DMEV2","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":"09f5054aed61732f5f8253ee099e4a1500aea068b9d6a2a0a2372700680f564a","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-07-19T09:27:04Z","title_canon_sha256":"6f4d5682f86a1ff72f83a255e53aa5656c4a864a6cf5be1ead4209eb075b8679"},"schema_version":"1.0","source":{"id":"math/0607453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607453","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607453v1","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607453","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"5CSXLKYCGZEU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5CSXLKYCGZEUUOXO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5CSXLKYC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8046bff83b6e3db112175cb99637c279defef77d67e6c914e21353c59233e61d","target":"graph","created_at":"2026-05-18T01:08:50Z","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":"We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp $\\LL\\_p$-mean error bounds, and laws of large numbers for $U$-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schr\\\"{o}dinger semigroups are al","authors_text":"Fr\\'ed\\'eric Patras (JAD), Pierre Del Moral (JAD), Sylvain Rubenthaler (JAD)","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-07-19T09:27:04Z","title":"Coalescent tree based functional representations for some Feynman-Kac particle models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607453","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":"sha256:301bfdc78787ce78f1eb362e13bbdd1e5f54a4c10e321bda3b0a926e50e4e6e2","target":"record","created_at":"2026-05-18T01:08:50Z","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":"09f5054aed61732f5f8253ee099e4a1500aea068b9d6a2a0a2372700680f564a","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-07-19T09:27:04Z","title_canon_sha256":"6f4d5682f86a1ff72f83a255e53aa5656c4a864a6cf5be1ead4209eb075b8679"},"schema_version":"1.0","source":{"id":"math/0607453","kind":"arxiv","version":1}},"canonical_sha256":"e8a575ab0236494a3aeedfcf2f8d84ae8adb19dafa6e989fc5474ad6cc3d38aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8a575ab0236494a3aeedfcf2f8d84ae8adb19dafa6e989fc5474ad6cc3d38aa","first_computed_at":"2026-05-18T01:08:50.002906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:50.002906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8in3+6ReYj0Xw0nfbs9Jo0ajpu6AXBWVlEgf4ldnGOO3TLVrUcwKX5U0SqKFyL8Jfb/HuVL41l9PV2UUhXbwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:50.003521Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:301bfdc78787ce78f1eb362e13bbdd1e5f54a4c10e321bda3b0a926e50e4e6e2","sha256:8046bff83b6e3db112175cb99637c279defef77d67e6c914e21353c59233e61d"],"state_sha256":"970da9759bd531e8c91b3ec71fb60a1747fcd1089c4c9865b2a9946448be8bf7"}