{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:O4O353ASGNUK7P47VAGXI6UGG6","short_pith_number":"pith:O4O353AS","canonical_record":{"source":{"id":"1606.06351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-06-20T22:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"5381c8d9e2983e230f3fc145441506dc3af41c1775fac448819a9ddc2bdd5c3f","abstract_canon_sha256":"4e5c91642f599a099ccd507f66d46d0adec6ab63b20dd5971c3bb76f29219f2a"},"schema_version":"1.0"},"canonical_sha256":"771dbeec123368afbf9fa80d747a8637b3bc385e41bb2200ab3a6fb268d84b4d","source":{"kind":"arxiv","id":"1606.06351","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06351","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06351v2","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06351","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"O4O353ASGNUK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O4O353ASGNUK7P47","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O4O353AS","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:O4O353ASGNUK7P47VAGXI6UGG6","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-06-20T22:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"5381c8d9e2983e230f3fc145441506dc3af41c1775fac448819a9ddc2bdd5c3f","abstract_canon_sha256":"4e5c91642f599a099ccd507f66d46d0adec6ab63b20dd5971c3bb76f29219f2a"},"schema_version":"1.0"},"canonical_sha256":"771dbeec123368afbf9fa80d747a8637b3bc385e41bb2200ab3a6fb268d84b4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:24.524340Z","signature_b64":"LjnZFUX2lRx9Cb8uW89j/zmGFFPvcJSK81SQHRyB0afvivC8t/Vgm9/VTAwWCMIOjzDlGVCil7xfiQz9WCAdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"771dbeec123368afbf9fa80d747a8637b3bc385e41bb2200ab3a6fb268d84b4d","last_reissued_at":"2026-05-18T00:49:24.523641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:24.523641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06351","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":"2026-05-18T00:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2wPztqqBfprJw+dJt3iTgDSWRrLEX9MbwYMfUc/vrS1HsC/V/TGTyTJvc14eJk/rOEbTMgt2LFOc34+z4EPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:31:48.567572Z"},"content_sha256":"ff84bffbfe264e7cb1c2d1a6480f468d6731a6891397f063c9ac25cb8a9dd547","schema_version":"1.0","event_id":"sha256:ff84bffbfe264e7cb1c2d1a6480f468d6731a6891397f063c9ac25cb8a9dd547"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:O4O353ASGNUK7P47VAGXI6UGG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric MCMC for Infinite-Dimensional Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Alexandros Beskos, Andrew M. Stuart, Mark Girolami, Patrick E. Farrell, Shiwei Lan","submitted_at":"2016-06-20T22:30:14Z","abstract_excerpt":"Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the poster"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06351","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":"2026-05-18T00:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j46U4ExfJ0N3vHnfo4PS2b2ZAQilLh/48wwA0CkuYb5Yi6inRQdmpvioKmzRjdJoeaku264nw8+ivyMIOJdsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:31:48.567922Z"},"content_sha256":"246e53a4e7fb37d91dba3c2ed720eaa8f7439876493f6e3a35e46ce590bc4438","schema_version":"1.0","event_id":"sha256:246e53a4e7fb37d91dba3c2ed720eaa8f7439876493f6e3a35e46ce590bc4438"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4O353ASGNUK7P47VAGXI6UGG6/bundle.json","state_url":"https://pith.science/pith/O4O353ASGNUK7P47VAGXI6UGG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4O353ASGNUK7P47VAGXI6UGG6/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":"2026-06-04T11:31:48Z","links":{"resolver":"https://pith.science/pith/O4O353ASGNUK7P47VAGXI6UGG6","bundle":"https://pith.science/pith/O4O353ASGNUK7P47VAGXI6UGG6/bundle.json","state":"https://pith.science/pith/O4O353ASGNUK7P47VAGXI6UGG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4O353ASGNUK7P47VAGXI6UGG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O4O353ASGNUK7P47VAGXI6UGG6","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":"4e5c91642f599a099ccd507f66d46d0adec6ab63b20dd5971c3bb76f29219f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-06-20T22:30:14Z","title_canon_sha256":"5381c8d9e2983e230f3fc145441506dc3af41c1775fac448819a9ddc2bdd5c3f"},"schema_version":"1.0","source":{"id":"1606.06351","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06351","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06351v2","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06351","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"O4O353ASGNUK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O4O353ASGNUK7P47","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O4O353AS","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:246e53a4e7fb37d91dba3c2ed720eaa8f7439876493f6e3a35e46ce590bc4438","target":"graph","created_at":"2026-05-18T00:49:24Z","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":"Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the poster","authors_text":"Alexandros Beskos, Andrew M. Stuart, Mark Girolami, Patrick E. Farrell, Shiwei Lan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-06-20T22:30:14Z","title":"Geometric MCMC for Infinite-Dimensional Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06351","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:ff84bffbfe264e7cb1c2d1a6480f468d6731a6891397f063c9ac25cb8a9dd547","target":"record","created_at":"2026-05-18T00:49:24Z","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":"4e5c91642f599a099ccd507f66d46d0adec6ab63b20dd5971c3bb76f29219f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-06-20T22:30:14Z","title_canon_sha256":"5381c8d9e2983e230f3fc145441506dc3af41c1775fac448819a9ddc2bdd5c3f"},"schema_version":"1.0","source":{"id":"1606.06351","kind":"arxiv","version":2}},"canonical_sha256":"771dbeec123368afbf9fa80d747a8637b3bc385e41bb2200ab3a6fb268d84b4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"771dbeec123368afbf9fa80d747a8637b3bc385e41bb2200ab3a6fb268d84b4d","first_computed_at":"2026-05-18T00:49:24.523641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:24.523641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjnZFUX2lRx9Cb8uW89j/zmGFFPvcJSK81SQHRyB0afvivC8t/Vgm9/VTAwWCMIOjzDlGVCil7xfiQz9WCAdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:24.524340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06351","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff84bffbfe264e7cb1c2d1a6480f468d6731a6891397f063c9ac25cb8a9dd547","sha256:246e53a4e7fb37d91dba3c2ed720eaa8f7439876493f6e3a35e46ce590bc4438"],"state_sha256":"868f32e79ae40d5ac596e78ef2bdfa42b5180651c1d7e8e6754a956cf190ba33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T8oX60P6hBGso5OPWSg6tPUeZPtx+bzkeeTcYD7KhOyLyp3YESl6EEGFiKZymgFR2YwdE//R1uLnKeZ0qrdrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:31:48.569879Z","bundle_sha256":"8436247379e42ed52579480cd230d2f4cf21a6fc3df61f07e5f098d7d0d140e5"}}