{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y2LDMSOBSV77CFGDZVNMYP7LFG","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":"89bddaf6f304a9a85f6e82feec31239e77c5a3ef05474fd2b92d47f2496d4a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-29T12:35:22Z","title_canon_sha256":"98f51f6ab6ef0f21d96de6a1fdbb8dada3f1930281aac0ff2db70ea97655eb46"},"schema_version":"1.0","source":{"id":"1311.7544","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7544","created_at":"2026-05-18T02:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7544v2","created_at":"2026-05-18T02:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7544","created_at":"2026-05-18T02:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"Y2LDMSOBSV77","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y2LDMSOBSV77CFGD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y2LDMSOB","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:7e82dfa4a2b6d200f850293c05827e9d9c364a41ab9f6373090fa5ccb28d5f6f","target":"graph","created_at":"2026-05-18T02:55:13Z","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"},"paper":{"abstract_excerpt":"In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in \\cite{MMinvent} which gives a possible answer to some questions formulated by Kac in \\cite{Kac1956}. We also present some related recent results about Kac's chaos and Kac's program obtained in \\cite{MMWchaos,HaurayMischler,KleberSphere} by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.","authors_text":"St\\'ephane Mischler (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-29T12:35:22Z","title":"Kac's chaos and Kac's program"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7544","kind":"arxiv","version":2},"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":"sha256:8b140978d67c2dd084df5de84c764bcfb5ff53b912502d6daceb1ad8ba5d7f9d","target":"record","created_at":"2026-05-18T02:55:13Z","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":"89bddaf6f304a9a85f6e82feec31239e77c5a3ef05474fd2b92d47f2496d4a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-29T12:35:22Z","title_canon_sha256":"98f51f6ab6ef0f21d96de6a1fdbb8dada3f1930281aac0ff2db70ea97655eb46"},"schema_version":"1.0","source":{"id":"1311.7544","kind":"arxiv","version":2}},"canonical_sha256":"c6963649c1957ff114c3cd5acc3feb29a7ca4f6f25a611a19eadeef92a39d434","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6963649c1957ff114c3cd5acc3feb29a7ca4f6f25a611a19eadeef92a39d434","first_computed_at":"2026-05-18T02:55:13.157781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:13.157781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GSOVauasYwJXUNzQLMkB0+ArlAYXbsyEdZ7rGp5OrOC5ctn97nI3hGCj5iwfCuiqqbmxuzjYr3vkAcXsAfGlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:13.158305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7544","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b140978d67c2dd084df5de84c764bcfb5ff53b912502d6daceb1ad8ba5d7f9d","sha256:7e82dfa4a2b6d200f850293c05827e9d9c364a41ab9f6373090fa5ccb28d5f6f"],"state_sha256":"b3fe4036b42e1c680adb0ed7d7b9fb432da5ef0642175155e4fc30a28f6fc88f"}