{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:BVKLEZNY7XXTZ3OMPXCWVQJTSX","short_pith_number":"pith:BVKLEZNY","canonical_record":{"source":{"id":"2203.00521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-01T15:04:49Z","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"title_canon_sha256":"42a98740176e962725fb05ba87184285d84d2e9762527a6210947e1e1028f782","abstract_canon_sha256":"311c0e020d55a368edf18498fcb3b67e14f30475af7017d534f58a42026dbc16"},"schema_version":"1.0"},"canonical_sha256":"0d54b265b8fdef3cedcc7dc56ac13395cedce0ec4bdec1a88af49283c55cb575","source":{"kind":"arxiv","id":"2203.00521","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.00521","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"2203.00521v3","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.00521","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"BVKLEZNY7XXT","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_16","alias_value":"BVKLEZNY7XXTZ3OM","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_8","alias_value":"BVKLEZNY","created_at":"2026-07-05T04:47:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:BVKLEZNY7XXTZ3OMPXCWVQJTSX","target":"record","payload":{"canonical_record":{"source":{"id":"2203.00521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-01T15:04:49Z","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"title_canon_sha256":"42a98740176e962725fb05ba87184285d84d2e9762527a6210947e1e1028f782","abstract_canon_sha256":"311c0e020d55a368edf18498fcb3b67e14f30475af7017d534f58a42026dbc16"},"schema_version":"1.0"},"canonical_sha256":"0d54b265b8fdef3cedcc7dc56ac13395cedce0ec4bdec1a88af49283c55cb575","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:47:26.814101Z","signature_b64":"Ydym15TJr3ZYLlyn1Z11aVbQsMBmJwLE/I0SXK6nSum4LEelV7i4A6HGYc2iHFKZguN71cEQwkrGGjOOx4qJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d54b265b8fdef3cedcc7dc56ac13395cedce0ec4bdec1a88af49283c55cb575","last_reissued_at":"2026-07-05T04:47:26.813696Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:47:26.813696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.00521","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:47:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XMttp7dzr89Wa2AZ34izD6sRJQhiF3DG6Be9LyJjSaKq4A+kyIJPgS60U7joGxFi3DJlRsdbyFmjZhJDX6MAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:52:39.703200Z"},"content_sha256":"eca9f26ad82ae65139fc47009136efe617771834a6768cd2ab0262db3a05eaeb","schema_version":"1.0","event_id":"sha256:eca9f26ad82ae65139fc47009136efe617771834a6768cd2ab0262db3a05eaeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:BVKLEZNY7XXTZ3OMPXCWVQJTSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Transformational Characterization of Unconditionally Equivalent Bayesian Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.CO","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Alex Markham, Danai Deligeorgaki, Liam Solus, Pratik Misra","submitted_at":"2022-03-01T15:04:49Z","abstract_excerpt":"We consider the problem of characterizing Bayesian networks up to unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the same set of unconditional $d$-separation statements. Each unconditional equivalence class (UEC) is uniquely represented with an undirected graph whose clique structure encodes the members of the class. Via this structure, we provide a transformational characterization of unconditional equivalence; i.e., we show that two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of specified moves. We also extend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.00521","kind":"arxiv","version":3},"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/2203.00521/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":"2026-07-05T04:47:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cKCHh6T/84u0DtoAsfn+bxp2MhU8lBgoD1zKxSZ/PoQZBSBssuZYfdVt3cyePq9/6l/UUWIx4bjUbSUqG6GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:52:39.703717Z"},"content_sha256":"20d0bc416d9f9c03b4b097e89d2dd0da3ca3a70594b1e4b992bad6b91649b76f","schema_version":"1.0","event_id":"sha256:20d0bc416d9f9c03b4b097e89d2dd0da3ca3a70594b1e4b992bad6b91649b76f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/bundle.json","state_url":"https://pith.science/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/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":"2026-08-03T15:52:39Z","links":{"resolver":"https://pith.science/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX","bundle":"https://pith.science/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/bundle.json","state":"https://pith.science/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVKLEZNY7XXTZ3OMPXCWVQJTSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BVKLEZNY7XXTZ3OMPXCWVQJTSX","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":"311c0e020d55a368edf18498fcb3b67e14f30475af7017d534f58a42026dbc16","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-01T15:04:49Z","title_canon_sha256":"42a98740176e962725fb05ba87184285d84d2e9762527a6210947e1e1028f782"},"schema_version":"1.0","source":{"id":"2203.00521","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.00521","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"2203.00521v3","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.00521","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"BVKLEZNY7XXT","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_16","alias_value":"BVKLEZNY7XXTZ3OM","created_at":"2026-07-05T04:47:26Z"},{"alias_kind":"pith_short_8","alias_value":"BVKLEZNY","created_at":"2026-07-05T04:47:26Z"}],"graph_snapshots":[{"event_id":"sha256:20d0bc416d9f9c03b4b097e89d2dd0da3ca3a70594b1e4b992bad6b91649b76f","target":"graph","created_at":"2026-07-05T04:47:26Z","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/2203.00521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of characterizing Bayesian networks up to unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the same set of unconditional $d$-separation statements. Each unconditional equivalence class (UEC) is uniquely represented with an undirected graph whose clique structure encodes the members of the class. Via this structure, we provide a transformational characterization of unconditional equivalence; i.e., we show that two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of specified moves. We also extend","authors_text":"Alex Markham, Danai Deligeorgaki, Liam Solus, Pratik Misra","cross_cats":["cs.LG","math.CO","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-01T15:04:49Z","title":"A Transformational Characterization of Unconditionally Equivalent Bayesian Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.00521","kind":"arxiv","version":3},"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:eca9f26ad82ae65139fc47009136efe617771834a6768cd2ab0262db3a05eaeb","target":"record","created_at":"2026-07-05T04:47:26Z","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":"311c0e020d55a368edf18498fcb3b67e14f30475af7017d534f58a42026dbc16","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-01T15:04:49Z","title_canon_sha256":"42a98740176e962725fb05ba87184285d84d2e9762527a6210947e1e1028f782"},"schema_version":"1.0","source":{"id":"2203.00521","kind":"arxiv","version":3}},"canonical_sha256":"0d54b265b8fdef3cedcc7dc56ac13395cedce0ec4bdec1a88af49283c55cb575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d54b265b8fdef3cedcc7dc56ac13395cedce0ec4bdec1a88af49283c55cb575","first_computed_at":"2026-07-05T04:47:26.813696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:26.813696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ydym15TJr3ZYLlyn1Z11aVbQsMBmJwLE/I0SXK6nSum4LEelV7i4A6HGYc2iHFKZguN71cEQwkrGGjOOx4qJDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:26.814101Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.00521","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eca9f26ad82ae65139fc47009136efe617771834a6768cd2ab0262db3a05eaeb","sha256:20d0bc416d9f9c03b4b097e89d2dd0da3ca3a70594b1e4b992bad6b91649b76f"],"state_sha256":"a15e08e0660d94940436d5e74eb682b507087dac59011aa87bccc91f8302d56e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoHb/BeML/a4QB+K8l/ijyZDfrs129XN2jcdx0bKZJOawfqZPQ6F61HA61X2zVGVyRXJ6tx+Q7RDQKvS2ltVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:52:39.707782Z","bundle_sha256":"45afad4100815838ae74da6fd1d5b76c910eb68b501caf540a26dc30e791a024"}}