{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:3DXQI5HDKUV5DB6VMKTTELIVKS","short_pith_number":"pith:3DXQI5HD","canonical_record":{"source":{"id":"math/0407120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-07-08T08:18:44Z","cross_cats_sorted":[],"title_canon_sha256":"fcaa0aba5b348bc02f3dcfca2b9609134945fbf85d391deae63047ea8e3cfbd1","abstract_canon_sha256":"152f6ff586a2de916a5f77a38a712093302e4e4d0174f3d983b8b53ddc4e7678"},"schema_version":"1.0"},"canonical_sha256":"d8ef0474e3552bd187d562a7322d1554b5e4cdb4fb7327fa488fd49e40d66239","source":{"kind":"arxiv","id":"math/0407120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407120","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407120v1","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407120","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"3DXQI5HDKUV5","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"3DXQI5HDKUV5DB6V","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"3DXQI5HD","created_at":"2026-07-04T14:38:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:3DXQI5HDKUV5DB6VMKTTELIVKS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0407120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-07-08T08:18:44Z","cross_cats_sorted":[],"title_canon_sha256":"fcaa0aba5b348bc02f3dcfca2b9609134945fbf85d391deae63047ea8e3cfbd1","abstract_canon_sha256":"152f6ff586a2de916a5f77a38a712093302e4e4d0174f3d983b8b53ddc4e7678"},"schema_version":"1.0"},"canonical_sha256":"d8ef0474e3552bd187d562a7322d1554b5e4cdb4fb7327fa488fd49e40d66239","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:53.998101Z","signature_b64":"efL8oO6zcwZphOxvoOsq0Umceh7ca1swkcHKm2B5kZ6GDWjSXTmJm8EyYmjmJrM+J2X6tLUgBL3aOtd4m01OCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8ef0474e3552bd187d562a7322d1554b5e4cdb4fb7327fa488fd49e40d66239","last_reissued_at":"2026-07-04T14:38:53.997676Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:53.997676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0407120","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":"2026-07-04T14:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3fQ3J9ZGD3fAOjn6F7DQ14YT9MOjNrvSl0TaE3nrQgSU/IXaFlHTJ3s8BpBpW1Q6BKM9Hpvh61SLyriHq3fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:06:55.257085Z"},"content_sha256":"24b3013de6982d5d7cfb7f90b3d300687dda36baf81ba777271f4c69c9e09e09","schema_version":"1.0","event_id":"sha256:24b3013de6982d5d7cfb7f90b3d300687dda36baf81ba777271f4c69c9e09e09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:3DXQI5HDKUV5DB6VMKTTELIVKS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A mixture representation of \\pi with applications in Markov chain Monte Carlo and perfect sampling","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian P. Robert, James P. Hobert","submitted_at":"2004-07-08T08:18:44Z","abstract_excerpt":"Let X={X_n:n=0,1,2,...} be an irreducible, positive recurrent Markov chain with invariant probability measure \\pi. We show that if X satisfies a one-step minorization condition, then \\pi can be represented as an infinite mixture. The distributions in the mixture are associated with the hitting times on an accessible atom introduced via the splitting construction of Athreya and Ney [Trans. Amer. Math. Soc. 245 (1978) 493-501] and Nummelin [Z. Wahrsch. Verw. Gebiete 43 (1978) 309-318]. When the small set in the minorization condition is the entire state space, our mixture representation of \\pi r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407120","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0407120/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFZUmybS1JA13Wk94544yi/ff2mBMDOeeDZPHfV1fg5HHe7/57SlE0hJCvFY79UEqsSt8wD5QuP8Yh5pXbCvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:06:55.257472Z"},"content_sha256":"110e4c75c362087147c81178c5d01509052a982eba549318fa6728e5a32db4fa","schema_version":"1.0","event_id":"sha256:110e4c75c362087147c81178c5d01509052a982eba549318fa6728e5a32db4fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/bundle.json","state_url":"https://pith.science/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/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":"2026-07-05T09:06:55Z","links":{"resolver":"https://pith.science/pith/3DXQI5HDKUV5DB6VMKTTELIVKS","bundle":"https://pith.science/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/bundle.json","state":"https://pith.science/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DXQI5HDKUV5DB6VMKTTELIVKS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:3DXQI5HDKUV5DB6VMKTTELIVKS","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":"152f6ff586a2de916a5f77a38a712093302e4e4d0174f3d983b8b53ddc4e7678","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-07-08T08:18:44Z","title_canon_sha256":"fcaa0aba5b348bc02f3dcfca2b9609134945fbf85d391deae63047ea8e3cfbd1"},"schema_version":"1.0","source":{"id":"math/0407120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407120","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407120v1","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407120","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"3DXQI5HDKUV5","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"3DXQI5HDKUV5DB6V","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"3DXQI5HD","created_at":"2026-07-04T14:38:53Z"}],"graph_snapshots":[{"event_id":"sha256:110e4c75c362087147c81178c5d01509052a982eba549318fa6728e5a32db4fa","target":"graph","created_at":"2026-07-04T14:38:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0407120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let X={X_n:n=0,1,2,...} be an irreducible, positive recurrent Markov chain with invariant probability measure \\pi. We show that if X satisfies a one-step minorization condition, then \\pi can be represented as an infinite mixture. The distributions in the mixture are associated with the hitting times on an accessible atom introduced via the splitting construction of Athreya and Ney [Trans. Amer. Math. Soc. 245 (1978) 493-501] and Nummelin [Z. Wahrsch. Verw. Gebiete 43 (1978) 309-318]. When the small set in the minorization condition is the entire state space, our mixture representation of \\pi r","authors_text":"Christian P. Robert, James P. Hobert","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-07-08T08:18:44Z","title":"A mixture representation of \\pi with applications in Markov chain Monte Carlo and perfect sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407120","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":"sha256:24b3013de6982d5d7cfb7f90b3d300687dda36baf81ba777271f4c69c9e09e09","target":"record","created_at":"2026-07-04T14:38:53Z","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":"152f6ff586a2de916a5f77a38a712093302e4e4d0174f3d983b8b53ddc4e7678","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-07-08T08:18:44Z","title_canon_sha256":"fcaa0aba5b348bc02f3dcfca2b9609134945fbf85d391deae63047ea8e3cfbd1"},"schema_version":"1.0","source":{"id":"math/0407120","kind":"arxiv","version":1}},"canonical_sha256":"d8ef0474e3552bd187d562a7322d1554b5e4cdb4fb7327fa488fd49e40d66239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8ef0474e3552bd187d562a7322d1554b5e4cdb4fb7327fa488fd49e40d66239","first_computed_at":"2026-07-04T14:38:53.997676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:53.997676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"efL8oO6zcwZphOxvoOsq0Umceh7ca1swkcHKm2B5kZ6GDWjSXTmJm8EyYmjmJrM+J2X6tLUgBL3aOtd4m01OCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:53.998101Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24b3013de6982d5d7cfb7f90b3d300687dda36baf81ba777271f4c69c9e09e09","sha256:110e4c75c362087147c81178c5d01509052a982eba549318fa6728e5a32db4fa"],"state_sha256":"a40df54f505125f37018382b10e6d6d8bb8254b8d8e9bd81aa4fd63e20bd3043"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vccZgHFH6jfsZqMZk19OBQ+Vd2WWmB7gBPIlESFRkjN6eGGoZYsyOz8BQr/jkETHq5ZmWH1v5O1PJlJ+uITgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:06:55.259365Z","bundle_sha256":"0b5f721ab84582e1c8c9c943292fdfda353bdd84226931d90e267cd84c6613b6"}}