{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HRH6DBRFZAV4TSDNYNMXQIUOKB","short_pith_number":"pith:HRH6DBRF","canonical_record":{"source":{"id":"1403.0408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-03T12:31:05Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"52ffdbfaead796b5fd27d23c2548d5acc71842cb2640a573a52f960102dbee8a","abstract_canon_sha256":"e3f5acaefc1a9dec79363a4c061bda5119c5f29b2d9c5d0189b2fb1472bb6fbd"},"schema_version":"1.0"},"canonical_sha256":"3c4fe18625c82bc9c86dc35978228e506c2e1317a5cb2970ccde302616a77bca","source":{"kind":"arxiv","id":"1403.0408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0408","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0408v2","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0408","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"HRH6DBRFZAV4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HRH6DBRFZAV4TSDN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HRH6DBRF","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HRH6DBRFZAV4TSDNYNMXQIUOKB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-03T12:31:05Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"52ffdbfaead796b5fd27d23c2548d5acc71842cb2640a573a52f960102dbee8a","abstract_canon_sha256":"e3f5acaefc1a9dec79363a4c061bda5119c5f29b2d9c5d0189b2fb1472bb6fbd"},"schema_version":"1.0"},"canonical_sha256":"3c4fe18625c82bc9c86dc35978228e506c2e1317a5cb2970ccde302616a77bca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:36.042065Z","signature_b64":"nn3Yr9P3SowcrHFr1WK9CQpO5ARosBdouZFcaMGHSm8/Iv1YjuBvQo+gX6QEaQK9k9DvLW7vk2qyClRoq6PeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c4fe18625c82bc9c86dc35978228e506c2e1317a5cb2970ccde302616a77bca","last_reissued_at":"2026-05-18T01:08:36.041519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:36.041519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0408","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":"2026-05-18T01:08:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+Ts8DDbIsi0wulXY3QES6W3QAsERfw3AP6PiqmuoE6Ga6tuv7dWZJwAIWuyclcsmbaA03YDVpDgTuxsr8EIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:45:46.996476Z"},"content_sha256":"7dc5640ec935229623f523ed67a0e3c95e7e80e26356827949c5e6460a1d86b3","schema_version":"1.0","event_id":"sha256:7dc5640ec935229623f523ed67a0e3c95e7e80e26356827949c5e6460a1d86b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HRH6DBRFZAV4TSDNYNMXQIUOKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Intersection Property of Conditional Independence and its Application to Causal Discovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.PR","authors_text":"Jonas Peters","submitted_at":"2014-03-03T12:31:05Z","abstract_excerpt":"This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent of $(A,B)$ given $C$. Under the assumption that the joint distribution has a continuous density, we provide necessary and sufficient conditions under which the intersection property holds. The result has direct applications to causal inference: it leads to strictly weaker conditions under which the graphical structure becomes identifiable from the joint dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0408","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":"2026-05-18T01:08:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Po/dt3P6y07u6VLTP77jkT5/C02DjxqtaTGJBOZxVP54tVAxSaImo5+tFFU6UB4N7cl4ixXJlGC8vfA2MUxyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:45:46.996835Z"},"content_sha256":"360dc6c7212b1c7a3c14fed32c4c5e00b1acb5a4a7a8bf41d66916d033a7980a","schema_version":"1.0","event_id":"sha256:360dc6c7212b1c7a3c14fed32c4c5e00b1acb5a4a7a8bf41d66916d033a7980a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/bundle.json","state_url":"https://pith.science/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/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":"2026-05-28T11:45:46Z","links":{"resolver":"https://pith.science/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB","bundle":"https://pith.science/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/bundle.json","state":"https://pith.science/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRH6DBRFZAV4TSDNYNMXQIUOKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HRH6DBRFZAV4TSDNYNMXQIUOKB","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":"e3f5acaefc1a9dec79363a4c061bda5119c5f29b2d9c5d0189b2fb1472bb6fbd","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-03T12:31:05Z","title_canon_sha256":"52ffdbfaead796b5fd27d23c2548d5acc71842cb2640a573a52f960102dbee8a"},"schema_version":"1.0","source":{"id":"1403.0408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0408","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0408v2","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0408","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"HRH6DBRFZAV4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HRH6DBRFZAV4TSDN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HRH6DBRF","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:360dc6c7212b1c7a3c14fed32c4c5e00b1acb5a4a7a8bf41d66916d033a7980a","target":"graph","created_at":"2026-05-18T01:08:36Z","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 work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent of $(A,B)$ given $C$. Under the assumption that the joint distribution has a continuous density, we provide necessary and sufficient conditions under which the intersection property holds. The result has direct applications to causal inference: it leads to strictly weaker conditions under which the graphical structure becomes identifiable from the joint dis","authors_text":"Jonas Peters","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-03T12:31:05Z","title":"On the Intersection Property of Conditional Independence and its Application to Causal Discovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0408","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":"sha256:7dc5640ec935229623f523ed67a0e3c95e7e80e26356827949c5e6460a1d86b3","target":"record","created_at":"2026-05-18T01:08:36Z","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":"e3f5acaefc1a9dec79363a4c061bda5119c5f29b2d9c5d0189b2fb1472bb6fbd","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-03T12:31:05Z","title_canon_sha256":"52ffdbfaead796b5fd27d23c2548d5acc71842cb2640a573a52f960102dbee8a"},"schema_version":"1.0","source":{"id":"1403.0408","kind":"arxiv","version":2}},"canonical_sha256":"3c4fe18625c82bc9c86dc35978228e506c2e1317a5cb2970ccde302616a77bca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c4fe18625c82bc9c86dc35978228e506c2e1317a5cb2970ccde302616a77bca","first_computed_at":"2026-05-18T01:08:36.041519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:36.041519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nn3Yr9P3SowcrHFr1WK9CQpO5ARosBdouZFcaMGHSm8/Iv1YjuBvQo+gX6QEaQK9k9DvLW7vk2qyClRoq6PeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:36.042065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dc5640ec935229623f523ed67a0e3c95e7e80e26356827949c5e6460a1d86b3","sha256:360dc6c7212b1c7a3c14fed32c4c5e00b1acb5a4a7a8bf41d66916d033a7980a"],"state_sha256":"ea043f1a6e51b2d10053eca61d96f834d000ddb3c5da36106c5c725ef143f19b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkLRTgZfmSqkJxZXZRjunWK+knNnAuIhdWVsm2fxqEprWRg/WGnRAKs2hhZZ2o+eNu1wBjBMVX4ZOGxX+J79DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:45:46.998805Z","bundle_sha256":"ebc5e59c98944efaba74bc9c59cbef96b147bc7bb63a3b0edd31e91e25c39018"}}