{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MRNRUPB4JLJVP4S3SAPXTZINWH","short_pith_number":"pith:MRNRUPB4","canonical_record":{"source":{"id":"1107.3046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-15T11:30:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a409882cbd477164c01553250e458c584c37c14017187f298e89e07bc0527753","abstract_canon_sha256":"5ec5482d0993b825c869231859963b293a65618d1a3338eb5130deac38d5d8bc"},"schema_version":"1.0"},"canonical_sha256":"645b1a3c3c4ad357f25b901f79e50db1eb3f5e1e153aad669609edb00e27779f","source":{"kind":"arxiv","id":"1107.3046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3046","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3046v1","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3046","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"MRNRUPB4JLJV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MRNRUPB4JLJVP4S3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MRNRUPB4","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MRNRUPB4JLJVP4S3SAPXTZINWH","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-15T11:30:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a409882cbd477164c01553250e458c584c37c14017187f298e89e07bc0527753","abstract_canon_sha256":"5ec5482d0993b825c869231859963b293a65618d1a3338eb5130deac38d5d8bc"},"schema_version":"1.0"},"canonical_sha256":"645b1a3c3c4ad357f25b901f79e50db1eb3f5e1e153aad669609edb00e27779f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:14.845801Z","signature_b64":"bcEMFrr/i+D+ghXe0VRPoxFmuC4A6x0ZXrIDwzmx1S4bXhkYdtI57H1RGLIeYOs9D3LruMAH82QmZLaEphG6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"645b1a3c3c4ad357f25b901f79e50db1eb3f5e1e153aad669609edb00e27779f","last_reissued_at":"2026-05-18T04:18:14.845170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:14.845170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3046","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":"2026-05-18T04:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xr6pawHvaHruf40Ip2pDpBcNKHwsaiK4AABJ65go1AxuU37CnjVRlInFQQuxqGK5iBnJmyB6XHwVAZxP5HWNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:25.828525Z"},"content_sha256":"ce8b1259fc8ced24e57351f53aff25c8c6df781e328bc49935a6076d2c4f04f3","schema_version":"1.0","event_id":"sha256:ce8b1259fc8ced24e57351f53aff25c8c6df781e328bc49935a6076d2c4f04f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MRNRUPB4JLJVP4S3SAPXTZINWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On nonlinear Markov chain Monte Carlo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ajay Jasra, Arnaud Doucet, Christophe Andrieu, Pierre Del Moral","submitted_at":"2011-07-15T11:30:37Z","abstract_excerpt":"Let $\\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure $\\pi\\in\\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae: Genealogical and Interacting Particle Systems with Applications (2004) Springer]) $K:\\mathscr{P}(E)\\times E\\rightarrow\\mathscr{P}(E)$ can be constructed to, in some sense, improve over MCMC methods. However, such nonlinear kernels cannot be simulated exactly, so approximations of the nonlinea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3046","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":"2026-05-18T04:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejcjosxHPZbvpJzKU7Ox/Bw8Nefaqzs+7U7W0osXmV/liUZd9O7PfLpfiZ2PgG3WIBdUSkf53UFJYUHJFHMOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:25.829193Z"},"content_sha256":"37e3731dd303b8fe4b2cdebbc6642ffaca4c305d18416fd62b1337896394e5b7","schema_version":"1.0","event_id":"sha256:37e3731dd303b8fe4b2cdebbc6642ffaca4c305d18416fd62b1337896394e5b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/bundle.json","state_url":"https://pith.science/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/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":"2026-05-28T23:38:25Z","links":{"resolver":"https://pith.science/pith/MRNRUPB4JLJVP4S3SAPXTZINWH","bundle":"https://pith.science/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/bundle.json","state":"https://pith.science/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRNRUPB4JLJVP4S3SAPXTZINWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MRNRUPB4JLJVP4S3SAPXTZINWH","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":"5ec5482d0993b825c869231859963b293a65618d1a3338eb5130deac38d5d8bc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-15T11:30:37Z","title_canon_sha256":"a409882cbd477164c01553250e458c584c37c14017187f298e89e07bc0527753"},"schema_version":"1.0","source":{"id":"1107.3046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3046","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3046v1","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3046","created_at":"2026-05-18T04:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"MRNRUPB4JLJV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MRNRUPB4JLJVP4S3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MRNRUPB4","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:37e3731dd303b8fe4b2cdebbc6642ffaca4c305d18416fd62b1337896394e5b7","target":"graph","created_at":"2026-05-18T04:18:14Z","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":"Let $\\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure $\\pi\\in\\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae: Genealogical and Interacting Particle Systems with Applications (2004) Springer]) $K:\\mathscr{P}(E)\\times E\\rightarrow\\mathscr{P}(E)$ can be constructed to, in some sense, improve over MCMC methods. However, such nonlinear kernels cannot be simulated exactly, so approximations of the nonlinea","authors_text":"Ajay Jasra, Arnaud Doucet, Christophe Andrieu, Pierre Del Moral","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-15T11:30:37Z","title":"On nonlinear Markov chain Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3046","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:ce8b1259fc8ced24e57351f53aff25c8c6df781e328bc49935a6076d2c4f04f3","target":"record","created_at":"2026-05-18T04:18:14Z","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":"5ec5482d0993b825c869231859963b293a65618d1a3338eb5130deac38d5d8bc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-15T11:30:37Z","title_canon_sha256":"a409882cbd477164c01553250e458c584c37c14017187f298e89e07bc0527753"},"schema_version":"1.0","source":{"id":"1107.3046","kind":"arxiv","version":1}},"canonical_sha256":"645b1a3c3c4ad357f25b901f79e50db1eb3f5e1e153aad669609edb00e27779f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"645b1a3c3c4ad357f25b901f79e50db1eb3f5e1e153aad669609edb00e27779f","first_computed_at":"2026-05-18T04:18:14.845170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:14.845170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bcEMFrr/i+D+ghXe0VRPoxFmuC4A6x0ZXrIDwzmx1S4bXhkYdtI57H1RGLIeYOs9D3LruMAH82QmZLaEphG6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:14.845801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce8b1259fc8ced24e57351f53aff25c8c6df781e328bc49935a6076d2c4f04f3","sha256:37e3731dd303b8fe4b2cdebbc6642ffaca4c305d18416fd62b1337896394e5b7"],"state_sha256":"7d2a35134de41120f5382529c358ca5f658add3e54a44bd303da414790343eb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIXphrhkkBKjESi8cidfiHfpOZLwnyht37MqOGwWkmoYe9UX7TbYBjfVtAxRCuEZnXX8z31OeA0tST38WbYJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:38:25.832966Z","bundle_sha256":"463a91da1e13c86a7f97582d512b84ce986f3163fd5c429be8d8790fdfc3f526"}}