{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EOW5XULC4QR7HY7SZM4E3F42KD","short_pith_number":"pith:EOW5XULC","canonical_record":{"source":{"id":"1705.00166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-04-29T10:49:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9edd360bb6227764256a0b67a6657970a53003741a073d10b1fe1c7cf391de71","abstract_canon_sha256":"6164687aed11260ccbea70f2acefc30e6a61a55772d88932605f85bd0bb18468"},"schema_version":"1.0"},"canonical_sha256":"23addbd162e423f3e3f2cb384d979a50ddb8c076eff12e3ee767ae3caeabacc7","source":{"kind":"arxiv","id":"1705.00166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00166","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00166v2","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00166","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"EOW5XULC4QR7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOW5XULC4QR7HY7S","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOW5XULC","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EOW5XULC4QR7HY7SZM4E3F42KD","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-04-29T10:49:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9edd360bb6227764256a0b67a6657970a53003741a073d10b1fe1c7cf391de71","abstract_canon_sha256":"6164687aed11260ccbea70f2acefc30e6a61a55772d88932605f85bd0bb18468"},"schema_version":"1.0"},"canonical_sha256":"23addbd162e423f3e3f2cb384d979a50ddb8c076eff12e3ee767ae3caeabacc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.127053Z","signature_b64":"4mKZXB++URfXxGG8oOabF93qf7WxF6vvbnwqUQInuiRA4ANO1mzzj/Dy5bXcXiAvnDPiUpnh2OmsnmWKRaXXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23addbd162e423f3e3f2cb384d979a50ddb8c076eff12e3ee767ae3caeabacc7","last_reissued_at":"2026-05-17T23:46:31.126336Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.126336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00166","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":"2026-05-17T23:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KXS3vIhbHLZ/5mlG8SftH5JeRouZkK70FoqUD6bXsp+HoNQTNvL9sF99wOaeAtH+7c0GqcC1KhiLjRSAb8pvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:17:29.629180Z"},"content_sha256":"5bfe52b67e9a3429e8824a02756758f973a82365d6999e1b7485602283ba7623","schema_version":"1.0","event_id":"sha256:5bfe52b67e9a3429e8824a02756758f973a82365d6999e1b7485602283ba7623"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EOW5XULC4QR7HY7SZM4E3F42KD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convergence of Hamiltonian Monte Carlo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"stat.CO","authors_text":"Alain Durmus, Eero Saksman, Eric Moulines","submitted_at":"2017-04-29T10:49:58Z","abstract_excerpt":"This paper discusses the irreducibility and geometric ergodicity of the Hamiltonian Monte Carlo (HMC) algorithm. We consider cases where the number of steps of the symplectic integrator is either fixed or random. Under mild conditions on the potential $\\F$ associated with target distribution $\\pi$, we first show that the Markov kernel associated to the HMC algorithm is irreducible and recurrent. Under more stringent conditions, we then establish that the Markov kernel is Harris recurrent. Finally, we provide verifiable conditions on $\\F$ under which the HMC sampler is geometrically ergodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00166","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":"2026-05-17T23:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2V2RIcxrVUYIfGDZLuzL7QWDYMjtV2f37GNFkxznQi+ayC4HJJEdHYnFV7eFi8cN9d6rBPyFxYwe4Nlw1XPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:17:29.629964Z"},"content_sha256":"3d9b33335bab1883b3bd3edcf2bc833fc7ec72cc230e2155aa4f228983abc4cf","schema_version":"1.0","event_id":"sha256:3d9b33335bab1883b3bd3edcf2bc833fc7ec72cc230e2155aa4f228983abc4cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOW5XULC4QR7HY7SZM4E3F42KD/bundle.json","state_url":"https://pith.science/pith/EOW5XULC4QR7HY7SZM4E3F42KD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOW5XULC4QR7HY7SZM4E3F42KD/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":"2026-08-11T06:17:29Z","links":{"resolver":"https://pith.science/pith/EOW5XULC4QR7HY7SZM4E3F42KD","bundle":"https://pith.science/pith/EOW5XULC4QR7HY7SZM4E3F42KD/bundle.json","state":"https://pith.science/pith/EOW5XULC4QR7HY7SZM4E3F42KD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOW5XULC4QR7HY7SZM4E3F42KD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EOW5XULC4QR7HY7SZM4E3F42KD","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":"6164687aed11260ccbea70f2acefc30e6a61a55772d88932605f85bd0bb18468","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-04-29T10:49:58Z","title_canon_sha256":"9edd360bb6227764256a0b67a6657970a53003741a073d10b1fe1c7cf391de71"},"schema_version":"1.0","source":{"id":"1705.00166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00166","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00166v2","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00166","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"EOW5XULC4QR7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOW5XULC4QR7HY7S","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOW5XULC","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:3d9b33335bab1883b3bd3edcf2bc833fc7ec72cc230e2155aa4f228983abc4cf","target":"graph","created_at":"2026-05-17T23:46:31Z","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":"This paper discusses the irreducibility and geometric ergodicity of the Hamiltonian Monte Carlo (HMC) algorithm. We consider cases where the number of steps of the symplectic integrator is either fixed or random. Under mild conditions on the potential $\\F$ associated with target distribution $\\pi$, we first show that the Markov kernel associated to the HMC algorithm is irreducible and recurrent. Under more stringent conditions, we then establish that the Markov kernel is Harris recurrent. Finally, we provide verifiable conditions on $\\F$ under which the HMC sampler is geometrically ergodic.","authors_text":"Alain Durmus, Eero Saksman, Eric Moulines","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-04-29T10:49:58Z","title":"On the convergence of Hamiltonian Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00166","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":"sha256:5bfe52b67e9a3429e8824a02756758f973a82365d6999e1b7485602283ba7623","target":"record","created_at":"2026-05-17T23:46:31Z","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":"6164687aed11260ccbea70f2acefc30e6a61a55772d88932605f85bd0bb18468","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-04-29T10:49:58Z","title_canon_sha256":"9edd360bb6227764256a0b67a6657970a53003741a073d10b1fe1c7cf391de71"},"schema_version":"1.0","source":{"id":"1705.00166","kind":"arxiv","version":2}},"canonical_sha256":"23addbd162e423f3e3f2cb384d979a50ddb8c076eff12e3ee767ae3caeabacc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23addbd162e423f3e3f2cb384d979a50ddb8c076eff12e3ee767ae3caeabacc7","first_computed_at":"2026-05-17T23:46:31.126336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:31.126336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4mKZXB++URfXxGG8oOabF93qf7WxF6vvbnwqUQInuiRA4ANO1mzzj/Dy5bXcXiAvnDPiUpnh2OmsnmWKRaXXBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:31.127053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bfe52b67e9a3429e8824a02756758f973a82365d6999e1b7485602283ba7623","sha256:3d9b33335bab1883b3bd3edcf2bc833fc7ec72cc230e2155aa4f228983abc4cf"],"state_sha256":"03600bcb9c8f61f00cb5057ff4fb30ed8b1797a0ed7853a435919a746596296f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YsViNhhrxXl0V+LKgU7ywvp+f1dnLhYFO9xHK6oylMiowcZMLuw4O0x2jKyquHUCK51pYWnjbqnA3TbucfH9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:17:29.635204Z","bundle_sha256":"9cb0743602d1704c5be59ac27b877e7b760d6c8332c90cdde90229faf7d52a89"}}