{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BQ4B6S27HLJ6KKQNKGYN2HKVBK","short_pith_number":"pith:BQ4B6S27","canonical_record":{"source":{"id":"1301.6624","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-28T17:49:56Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"cdd923bf810c68a48b24d43a4317022c4347341ae48978b718f956333d8a6c0d","abstract_canon_sha256":"b7b618a5a735751174fd1f4d8dc83f65a8068450a18e6b03d692beb7cf5e8643"},"schema_version":"1.0"},"canonical_sha256":"0c381f4b5f3ad3e52a0d51b0dd1d550a9cc1114426145173daf6140e492e5b9c","source":{"kind":"arxiv","id":"1301.6624","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6624","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6624v4","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6624","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"BQ4B6S27HLJ6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQ4B6S27HLJ6KKQN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQ4B6S27","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BQ4B6S27HLJ6KKQNKGYN2HKVBK","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6624","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-28T17:49:56Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"cdd923bf810c68a48b24d43a4317022c4347341ae48978b718f956333d8a6c0d","abstract_canon_sha256":"b7b618a5a735751174fd1f4d8dc83f65a8068450a18e6b03d692beb7cf5e8643"},"schema_version":"1.0"},"canonical_sha256":"0c381f4b5f3ad3e52a0d51b0dd1d550a9cc1114426145173daf6140e492e5b9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:14.810498Z","signature_b64":"PlnMvBcnNAoIcKp9/bWJIGnh+TujXE/b+uJkqYLv9DdlTCy9wrEnBPyf/jtOflHrNREajBRTQFP43IDtpZf9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c381f4b5f3ad3e52a0d51b0dd1d550a9cc1114426145173daf6140e492e5b9c","last_reissued_at":"2026-05-18T02:45:14.809889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:14.809889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6624","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"77HK2iG5t+v1yD2ZjLlA5KEDNAlOd+jjQb7aLRHgoh4xZlAswMSfJ/JpNzVpbyN3l+/qMSIxgRXr65Qdp2wFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:45:26.640039Z"},"content_sha256":"c9dd548c9eb73e23fd5a340dc065c1cde5c4058cf150db150b014ed3cdf09765","schema_version":"1.0","event_id":"sha256:c9dd548c9eb73e23fd5a340dc065c1cde5c4058cf150db150b014ed3cdf09765"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BQ4B6S27HLJ6KKQNKGYN2HKVBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markovian acyclic directed mixed graphs for discrete data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Robin J. Evans, Thomas S. Richardson","submitted_at":"2013-01-28T17:49:56Z","abstract_excerpt":"Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\\rightarrow$) and bidirected ($\\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6624","kind":"arxiv","version":4},"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":"2026-05-18T02:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4MvEn3rwRME8GnTwq+zbP7rZfcVODnoBKj8zXpUMJ8m9++qkM7NVyPwt+h110C/IsZtJPhdRg2BfG0j7xaEbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:45:26.640450Z"},"content_sha256":"438d8f71e6c92db6074f682399cb077d21b96f8284746b244a15f48eb0469486","schema_version":"1.0","event_id":"sha256:438d8f71e6c92db6074f682399cb077d21b96f8284746b244a15f48eb0469486"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/bundle.json","state_url":"https://pith.science/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/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":"2026-06-04T08:45:26Z","links":{"resolver":"https://pith.science/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK","bundle":"https://pith.science/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/bundle.json","state":"https://pith.science/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQ4B6S27HLJ6KKQNKGYN2HKVBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BQ4B6S27HLJ6KKQNKGYN2HKVBK","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":"b7b618a5a735751174fd1f4d8dc83f65a8068450a18e6b03d692beb7cf5e8643","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-28T17:49:56Z","title_canon_sha256":"cdd923bf810c68a48b24d43a4317022c4347341ae48978b718f956333d8a6c0d"},"schema_version":"1.0","source":{"id":"1301.6624","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6624","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6624v4","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6624","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"BQ4B6S27HLJ6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQ4B6S27HLJ6KKQN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQ4B6S27","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:438d8f71e6c92db6074f682399cb077d21b96f8284746b244a15f48eb0469486","target":"graph","created_at":"2026-05-18T02:45:14Z","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":"Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\\rightarrow$) and bidirected ($\\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that ge","authors_text":"Robin J. Evans, Thomas S. Richardson","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-28T17:49:56Z","title":"Markovian acyclic directed mixed graphs for discrete data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6624","kind":"arxiv","version":4},"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:c9dd548c9eb73e23fd5a340dc065c1cde5c4058cf150db150b014ed3cdf09765","target":"record","created_at":"2026-05-18T02:45:14Z","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":"b7b618a5a735751174fd1f4d8dc83f65a8068450a18e6b03d692beb7cf5e8643","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-28T17:49:56Z","title_canon_sha256":"cdd923bf810c68a48b24d43a4317022c4347341ae48978b718f956333d8a6c0d"},"schema_version":"1.0","source":{"id":"1301.6624","kind":"arxiv","version":4}},"canonical_sha256":"0c381f4b5f3ad3e52a0d51b0dd1d550a9cc1114426145173daf6140e492e5b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c381f4b5f3ad3e52a0d51b0dd1d550a9cc1114426145173daf6140e492e5b9c","first_computed_at":"2026-05-18T02:45:14.809889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:14.809889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlnMvBcnNAoIcKp9/bWJIGnh+TujXE/b+uJkqYLv9DdlTCy9wrEnBPyf/jtOflHrNREajBRTQFP43IDtpZf9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:14.810498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6624","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9dd548c9eb73e23fd5a340dc065c1cde5c4058cf150db150b014ed3cdf09765","sha256:438d8f71e6c92db6074f682399cb077d21b96f8284746b244a15f48eb0469486"],"state_sha256":"5528402a94b9729bcb0c5fadca7667d75fd9cba09cbb5d3c40c9f51ea59ed19a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xuvOVzjCn+ZJ4mtINRz3/aJvqyFZsrGECZye0HghAmk3hAiZRN8KkcDEgRJWFAwBZniNd2P7NJ82dS9aBRRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:45:26.642900Z","bundle_sha256":"1f76dfcc0bcbe4447b0ca1faff51c9bbc366aaeb8be7ae35a3cea3a987f46104"}}