{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E24WGVMF42QDUYEEHQX5FQURSJ","short_pith_number":"pith:E24WGVMF","canonical_record":{"source":{"id":"1311.6300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-25T13:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"765a63e2a46a4005b722981d16ea9cab222537ae6040490ca44e78fb36a56ba2","abstract_canon_sha256":"0e6b06e82120e90a43beba3994ca96532204b845cde5ff94e883a562cafebf5c"},"schema_version":"1.0"},"canonical_sha256":"26b9635585e6a03a60843c2fd2c291926a1c867f27f9072294baf1ba6e24b452","source":{"kind":"arxiv","id":"1311.6300","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6300","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6300v2","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6300","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"E24WGVMF42QD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E24WGVMF42QDUYEE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E24WGVMF","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E24WGVMF42QDUYEEHQX5FQURSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-25T13:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"765a63e2a46a4005b722981d16ea9cab222537ae6040490ca44e78fb36a56ba2","abstract_canon_sha256":"0e6b06e82120e90a43beba3994ca96532204b845cde5ff94e883a562cafebf5c"},"schema_version":"1.0"},"canonical_sha256":"26b9635585e6a03a60843c2fd2c291926a1c867f27f9072294baf1ba6e24b452","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:44.677269Z","signature_b64":"kpVcTWBfYVCAKdZEMEeC9yJal+JXCB/82Ldqxdv5srU/L/3bxIS6ODtc4eF4jFL6DN3ryDEm9VYfmf9bVWvyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26b9635585e6a03a60843c2fd2c291926a1c867f27f9072294baf1ba6e24b452","last_reissued_at":"2026-05-18T02:47:44.676434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:44.676434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6300","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"027V0BijEyLcmsWlTYp6rh8Sp2FPcJRWKydhVNJKHDSrAQ0B/yjWoGubAM3CdnkZrt+MvivfzMsbi49EyhPFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:24:21.576595Z"},"content_sha256":"dec9c69da20b53b58e63797a663678fbe860b36b47637d175903abf9ab558784","schema_version":"1.0","event_id":"sha256:dec9c69da20b53b58e63797a663678fbe860b36b47637d175903abf9ab558784"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E24WGVMF42QDUYEEHQX5FQURSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A McKean optimal transportation perspective on Feynman-Kac formulae with application to data assimilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastian Reich, Yuan Cheng","submitted_at":"2013-11-25T13:44:34Z","abstract_excerpt":"Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this paper we focus on the sequential nature of many data assimilation problems and their numerical implementation in form of Monte Carlo methods. We demonstrate how sequential data assimilation can be interpreted as time-dependent Markov processes, which is often referred to as the McKean approach to Feynman-Kac formulae. It is shown that the McKean approach ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6300","kind":"arxiv","version":2},"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":"2026-05-18T02:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bSIqOGOudIdCVbVpGkrMxRIQ39xQm6jHWILtXOzo2XMBu3KH+F4ICwA0RTcN7nMXd03RXthf3ZpguosdmVWeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:24:21.576943Z"},"content_sha256":"98b1d1ba195d29e1ba3f2fff58cd0a81b367c4a404511ffb9a550d43f8b04b53","schema_version":"1.0","event_id":"sha256:98b1d1ba195d29e1ba3f2fff58cd0a81b367c4a404511ffb9a550d43f8b04b53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E24WGVMF42QDUYEEHQX5FQURSJ/bundle.json","state_url":"https://pith.science/pith/E24WGVMF42QDUYEEHQX5FQURSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E24WGVMF42QDUYEEHQX5FQURSJ/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":"2026-06-02T09:24:21Z","links":{"resolver":"https://pith.science/pith/E24WGVMF42QDUYEEHQX5FQURSJ","bundle":"https://pith.science/pith/E24WGVMF42QDUYEEHQX5FQURSJ/bundle.json","state":"https://pith.science/pith/E24WGVMF42QDUYEEHQX5FQURSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E24WGVMF42QDUYEEHQX5FQURSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E24WGVMF42QDUYEEHQX5FQURSJ","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":"0e6b06e82120e90a43beba3994ca96532204b845cde5ff94e883a562cafebf5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-25T13:44:34Z","title_canon_sha256":"765a63e2a46a4005b722981d16ea9cab222537ae6040490ca44e78fb36a56ba2"},"schema_version":"1.0","source":{"id":"1311.6300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6300","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6300v2","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6300","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"E24WGVMF42QD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E24WGVMF42QDUYEE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E24WGVMF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:98b1d1ba195d29e1ba3f2fff58cd0a81b367c4a404511ffb9a550d43f8b04b53","target":"graph","created_at":"2026-05-18T02:47:44Z","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":"Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this paper we focus on the sequential nature of many data assimilation problems and their numerical implementation in form of Monte Carlo methods. We demonstrate how sequential data assimilation can be interpreted as time-dependent Markov processes, which is often referred to as the McKean approach to Feynman-Kac formulae. It is shown that the McKean approach ha","authors_text":"Sebastian Reich, Yuan Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-25T13:44:34Z","title":"A McKean optimal transportation perspective on Feynman-Kac formulae with application to data assimilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6300","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:dec9c69da20b53b58e63797a663678fbe860b36b47637d175903abf9ab558784","target":"record","created_at":"2026-05-18T02:47:44Z","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":"0e6b06e82120e90a43beba3994ca96532204b845cde5ff94e883a562cafebf5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-25T13:44:34Z","title_canon_sha256":"765a63e2a46a4005b722981d16ea9cab222537ae6040490ca44e78fb36a56ba2"},"schema_version":"1.0","source":{"id":"1311.6300","kind":"arxiv","version":2}},"canonical_sha256":"26b9635585e6a03a60843c2fd2c291926a1c867f27f9072294baf1ba6e24b452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26b9635585e6a03a60843c2fd2c291926a1c867f27f9072294baf1ba6e24b452","first_computed_at":"2026-05-18T02:47:44.676434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:44.676434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpVcTWBfYVCAKdZEMEeC9yJal+JXCB/82Ldqxdv5srU/L/3bxIS6ODtc4eF4jFL6DN3ryDEm9VYfmf9bVWvyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:44.677269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dec9c69da20b53b58e63797a663678fbe860b36b47637d175903abf9ab558784","sha256:98b1d1ba195d29e1ba3f2fff58cd0a81b367c4a404511ffb9a550d43f8b04b53"],"state_sha256":"82aab8b3c8dfe99334ebcd32e40a5dcfa5d46d15dda460ea397121e754aa62aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfBepQ8sYnnNVanmB7GweNBVRanrWTO99iFS/Ss2wpKw56BEMefTBeyItAiI92F9FRRlhrQxYSX3oLZ6UxF9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:24:21.578952Z","bundle_sha256":"eb66ab852aca6079394b31878ded6e77ec7a18578a65ed881e0d5bfa2653f1c2"}}