{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZXLYZQU3EVYXRXQIUESOPWXG34","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":"1f1ce014d38f174b1c8e3d2a7267e698a7ed1e652800c5a6e4c62fc49149525e","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-12-18T06:15:19Z","title_canon_sha256":"b833287290c46f318c1ab662853aab1abf488844abe81140a654c00287ed7eda"},"schema_version":"1.0","source":{"id":"1112.4118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4118","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4118v1","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4118","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZXLYZQU3EVYX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZXLYZQU3EVYXRXQI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZXLYZQU3","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:d54d3a16707aa6795eab52440dd1dfc94fa98ce9c743f30f13de8f6ebbca0a2b","target":"graph","created_at":"2026-05-18T04:06:06Z","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":"With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By examining both the symplectic geometry underlying Hamiltonian dynamics and the requirements of Markov Chain Monte Carlo, we construct the general form of admissible Hamiltonians and propose a particular choice with potential application in Bayesian inference.","authors_text":"Leo C. Stein, Michael Betancourt","cross_cats":["physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-12-18T06:15:19Z","title":"The Geometry of Hamiltonian Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4118","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:ec78e8d3b7ceaf1640b9d85e6d48fe37dc5898572dcc9c181ca368e77881e996","target":"record","created_at":"2026-05-18T04:06:06Z","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":"1f1ce014d38f174b1c8e3d2a7267e698a7ed1e652800c5a6e4c62fc49149525e","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-12-18T06:15:19Z","title_canon_sha256":"b833287290c46f318c1ab662853aab1abf488844abe81140a654c00287ed7eda"},"schema_version":"1.0","source":{"id":"1112.4118","kind":"arxiv","version":1}},"canonical_sha256":"cdd78cc29b257178de08a124e7dae6df040d62d86fa7152de310fa028fbdeb4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdd78cc29b257178de08a124e7dae6df040d62d86fa7152de310fa028fbdeb4e","first_computed_at":"2026-05-18T04:06:06.996863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:06.996863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IsBcemmlN6rTTh/g7k5UAa46314enYTklYcGsNtP51+UtzVbKicJ2nKhLgItm4HekKXLbm1CRiGKjL5IlRC6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:06.997303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec78e8d3b7ceaf1640b9d85e6d48fe37dc5898572dcc9c181ca368e77881e996","sha256:d54d3a16707aa6795eab52440dd1dfc94fa98ce9c743f30f13de8f6ebbca0a2b"],"state_sha256":"492a193ecb218635f9c2088974f82e8077df65cf7846fd885bc15c265fe8b8e7"}