{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3KZYLC2OLB26NGO6IS2T2WWLT4","short_pith_number":"pith:3KZYLC2O","canonical_record":{"source":{"id":"1207.1376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-04T16:08:28Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"b3033a5f5020effa5329db7e637c60529b415ac11481ae1286b4b45a46ddb736","abstract_canon_sha256":"ce5620e9850471be8a31cda9a466cf34d11a4acfb311f1a07e143a6eabff42de"},"schema_version":"1.0"},"canonical_sha256":"dab3858b4e5875e699de44b53d5acb9f08f32f2ce788f6bd2425cfa2771b6988","source":{"kind":"arxiv","id":"1207.1376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1376","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1376v1","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1376","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"3KZYLC2OLB26","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KZYLC2OLB26NGO6","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KZYLC2O","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3KZYLC2OLB26NGO6IS2T2WWLT4","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-04T16:08:28Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"b3033a5f5020effa5329db7e637c60529b415ac11481ae1286b4b45a46ddb736","abstract_canon_sha256":"ce5620e9850471be8a31cda9a466cf34d11a4acfb311f1a07e143a6eabff42de"},"schema_version":"1.0"},"canonical_sha256":"dab3858b4e5875e699de44b53d5acb9f08f32f2ce788f6bd2425cfa2771b6988","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:37.551552Z","signature_b64":"6rQZnE3lfseWvBD62ZL0mw0/r3AW1H7zsjiLLvGxS0i1L1EahC74WHpACHfw8WTKfTUl1BAZDygDdR6j7tehDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dab3858b4e5875e699de44b53d5acb9f08f32f2ce788f6bd2425cfa2771b6988","last_reissued_at":"2026-05-18T03:51:37.550824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:37.550824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1376","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":"2026-05-18T03:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jnBqBLkh7vCo4Ca6XEQkXUBQNLj/BHnSN7e15C5tDvvaK5Yn6oSq8d5D/WKTYkYI6yUj6mpzpInBmhuD+aoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:36:58.594124Z"},"content_sha256":"48b565d8023332c9fc839afe9f6a959bd359a4bc268ddcc1d28d738eb6272ac5","schema_version":"1.0","event_id":"sha256:48b565d8023332c9fc839afe9f6a959bd359a4bc268ddcc1d28d738eb6272ac5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3KZYLC2OLB26NGO6IS2T2WWLT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counterfactual Reasoning in Linear Structural Equation Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"cs.AI","authors_text":"Manabu Kuroki, Zhihong Cai","submitted_at":"2012-07-04T16:08:28Z","abstract_excerpt":"Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a treatment variable were assigned to some value (counterfactually), given that a set of variables is observed (actually). In order to achieve this aim, we reformulate the formulas of the counterfactual distribution proposed by Balke and Pearl (1995) through both the total effects and a covariance matrix of observed variables. We further extend the framework of Balk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1376","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":""},"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":"2026-05-18T03:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2DHHv1c0uU1OOLcKeCCn4LpzFZnJ5pn+JeRTtM6zb/HQrrYeAiTLTUbGpaJf+oibo/gPMCCx56UW0onsQV8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:36:58.594470Z"},"content_sha256":"b3d72918ad1d8e7f4dbbc3dba60e99cf5ebe1abf1b59d836ae4b808eccae0916","schema_version":"1.0","event_id":"sha256:b3d72918ad1d8e7f4dbbc3dba60e99cf5ebe1abf1b59d836ae4b808eccae0916"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/bundle.json","state_url":"https://pith.science/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/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":"2026-06-27T06:36:58Z","links":{"resolver":"https://pith.science/pith/3KZYLC2OLB26NGO6IS2T2WWLT4","bundle":"https://pith.science/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/bundle.json","state":"https://pith.science/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KZYLC2OLB26NGO6IS2T2WWLT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3KZYLC2OLB26NGO6IS2T2WWLT4","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":"ce5620e9850471be8a31cda9a466cf34d11a4acfb311f1a07e143a6eabff42de","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-04T16:08:28Z","title_canon_sha256":"b3033a5f5020effa5329db7e637c60529b415ac11481ae1286b4b45a46ddb736"},"schema_version":"1.0","source":{"id":"1207.1376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1376","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1376v1","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1376","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"3KZYLC2OLB26","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KZYLC2OLB26NGO6","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KZYLC2O","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:b3d72918ad1d8e7f4dbbc3dba60e99cf5ebe1abf1b59d836ae4b808eccae0916","target":"graph","created_at":"2026-05-18T03:51:37Z","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":"Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a treatment variable were assigned to some value (counterfactually), given that a set of variables is observed (actually). In order to achieve this aim, we reformulate the formulas of the counterfactual distribution proposed by Balke and Pearl (1995) through both the total effects and a covariance matrix of observed variables. We further extend the framework of Balk","authors_text":"Manabu Kuroki, Zhihong Cai","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-04T16:08:28Z","title":"Counterfactual Reasoning in Linear Structural Equation Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1376","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":"sha256:48b565d8023332c9fc839afe9f6a959bd359a4bc268ddcc1d28d738eb6272ac5","target":"record","created_at":"2026-05-18T03:51:37Z","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":"ce5620e9850471be8a31cda9a466cf34d11a4acfb311f1a07e143a6eabff42de","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-07-04T16:08:28Z","title_canon_sha256":"b3033a5f5020effa5329db7e637c60529b415ac11481ae1286b4b45a46ddb736"},"schema_version":"1.0","source":{"id":"1207.1376","kind":"arxiv","version":1}},"canonical_sha256":"dab3858b4e5875e699de44b53d5acb9f08f32f2ce788f6bd2425cfa2771b6988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dab3858b4e5875e699de44b53d5acb9f08f32f2ce788f6bd2425cfa2771b6988","first_computed_at":"2026-05-18T03:51:37.550824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:37.550824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rQZnE3lfseWvBD62ZL0mw0/r3AW1H7zsjiLLvGxS0i1L1EahC74WHpACHfw8WTKfTUl1BAZDygDdR6j7tehDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:37.551552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48b565d8023332c9fc839afe9f6a959bd359a4bc268ddcc1d28d738eb6272ac5","sha256:b3d72918ad1d8e7f4dbbc3dba60e99cf5ebe1abf1b59d836ae4b808eccae0916"],"state_sha256":"9abf425eeb985b2134c433cd053c687e6dcd534544c99d526c565d5dfaecc468"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EdCgbo1PqHU4P/nILNX0axp8c+cNuJXIH5RBmLbryPtr+CZdd4yc/qlc9CulW0Pbm/vcbW+R5nJteeAxcisBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:36:58.596279Z","bundle_sha256":"7a2148810bf4d1225bfbeb5c2114389394a152df5b0f3ea1b323d2e9370beb98"}}