{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:MSRK5H7362Q6J7XHCNE3QKB7VZ","short_pith_number":"pith:MSRK5H73","canonical_record":{"source":{"id":"0908.0162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-08-02T21:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"56e7cbdd81a2edc3a5613c05ec0d5f4ca7f75320a0e36928cf8a37c9222c78cc","abstract_canon_sha256":"89251e6e2bf8c98d229197844c99f0d81f13840c90f48038144ac518b68d795a"},"schema_version":"1.0"},"canonical_sha256":"64a2ae9ffbf6a1e4fee71349b8283fae5e033ac0f815ef5e5f341017e822ea1f","source":{"kind":"arxiv","id":"0908.0162","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0162","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0162v3","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0162","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"MSRK5H7362Q6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MSRK5H7362Q6J7XH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MSRK5H73","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:MSRK5H7362Q6J7XHCNE3QKB7VZ","target":"record","payload":{"canonical_record":{"source":{"id":"0908.0162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-08-02T21:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"56e7cbdd81a2edc3a5613c05ec0d5f4ca7f75320a0e36928cf8a37c9222c78cc","abstract_canon_sha256":"89251e6e2bf8c98d229197844c99f0d81f13840c90f48038144ac518b68d795a"},"schema_version":"1.0"},"canonical_sha256":"64a2ae9ffbf6a1e4fee71349b8283fae5e033ac0f815ef5e5f341017e822ea1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:53.269923Z","signature_b64":"mo2MZHCUzskPsRqLrKbkfNCdLGaeJf2SZjqegXPprsDzRL3jNHLUUnc+iHWyOJL9nAb6bGUKC317cn/Bh3iFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64a2ae9ffbf6a1e4fee71349b8283fae5e033ac0f815ef5e5f341017e822ea1f","last_reissued_at":"2026-05-18T04:24:53.269461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:53.269461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.0162","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2M/frgtt8ZHzHY9xGln80ykn8yGMPG+aIARikmXZrmc40IuFWpOO3WNcAx1iH3r9wIby/K54OBPEduNpNeUPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:27:55.838125Z"},"content_sha256":"0ae6134250fee9d0c44808efa608fdb04b3f575dd1e04e1ccabbe540742878ee","schema_version":"1.0","event_id":"sha256:0ae6134250fee9d0c44808efa608fdb04b3f575dd1e04e1ccabbe540742878ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:MSRK5H7362Q6J7XHCNE3QKB7VZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling conditioned hypoelliptic diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew M. Stuart, Jochen Voss, Martin Hairer","submitted_at":"2009-08-02T21:30:31Z","abstract_excerpt":"A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this methodology to allow the construction of SPDEs which are invariant with respect to the distribution of a class of hypoelliptic diffusion processes, subject to a bridge conditioning, leading to SPDEs which are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0162","kind":"arxiv","version":3},"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":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ly1gJquzyMF5kn2WMUCwGaSRON0P3JFAtjt8nDnPx+8BECDRtsHJs3OLOzA2JQm6Mg2g9CvMJn0Rl6O9a8xcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:27:55.838487Z"},"content_sha256":"04d3fcfd9c393845cd4330163fa450168027a5ce95df6d4f6342e04d7d874561","schema_version":"1.0","event_id":"sha256:04d3fcfd9c393845cd4330163fa450168027a5ce95df6d4f6342e04d7d874561"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/bundle.json","state_url":"https://pith.science/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/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":"2026-06-04T11:27:55Z","links":{"resolver":"https://pith.science/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ","bundle":"https://pith.science/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/bundle.json","state":"https://pith.science/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSRK5H7362Q6J7XHCNE3QKB7VZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MSRK5H7362Q6J7XHCNE3QKB7VZ","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":"89251e6e2bf8c98d229197844c99f0d81f13840c90f48038144ac518b68d795a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-08-02T21:30:31Z","title_canon_sha256":"56e7cbdd81a2edc3a5613c05ec0d5f4ca7f75320a0e36928cf8a37c9222c78cc"},"schema_version":"1.0","source":{"id":"0908.0162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0162","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0162v3","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0162","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"MSRK5H7362Q6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MSRK5H7362Q6J7XH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MSRK5H73","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:04d3fcfd9c393845cd4330163fa450168027a5ce95df6d4f6342e04d7d874561","target":"graph","created_at":"2026-05-18T04:24:53Z","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":"A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this methodology to allow the construction of SPDEs which are invariant with respect to the distribution of a class of hypoelliptic diffusion processes, subject to a bridge conditioning, leading to SPDEs which are","authors_text":"Andrew M. Stuart, Jochen Voss, Martin Hairer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-08-02T21:30:31Z","title":"Sampling conditioned hypoelliptic diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0162","kind":"arxiv","version":3},"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":"sha256:0ae6134250fee9d0c44808efa608fdb04b3f575dd1e04e1ccabbe540742878ee","target":"record","created_at":"2026-05-18T04:24:53Z","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":"89251e6e2bf8c98d229197844c99f0d81f13840c90f48038144ac518b68d795a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-08-02T21:30:31Z","title_canon_sha256":"56e7cbdd81a2edc3a5613c05ec0d5f4ca7f75320a0e36928cf8a37c9222c78cc"},"schema_version":"1.0","source":{"id":"0908.0162","kind":"arxiv","version":3}},"canonical_sha256":"64a2ae9ffbf6a1e4fee71349b8283fae5e033ac0f815ef5e5f341017e822ea1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64a2ae9ffbf6a1e4fee71349b8283fae5e033ac0f815ef5e5f341017e822ea1f","first_computed_at":"2026-05-18T04:24:53.269461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.269461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mo2MZHCUzskPsRqLrKbkfNCdLGaeJf2SZjqegXPprsDzRL3jNHLUUnc+iHWyOJL9nAb6bGUKC317cn/Bh3iFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.269923Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ae6134250fee9d0c44808efa608fdb04b3f575dd1e04e1ccabbe540742878ee","sha256:04d3fcfd9c393845cd4330163fa450168027a5ce95df6d4f6342e04d7d874561"],"state_sha256":"fa8b50746503fd9ee8e74c041e1dba1ed36d79f52d74dc37b8cd5f6e5324c116"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stNPZI7dGCt5laWcbCUrvheI5fay/ZIOV7Oz/hGHIvDGC1/ypnd5uOLe2aWHrIK6+feTt57I7hLIhIajd4YTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:27:55.840968Z","bundle_sha256":"6fd3458b000a66329da9bc608aaf54c1c0da9d9b38b6c0bb2c77bfef86072adf"}}