{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ASBIBJGZNUWGTQUJ72OZQ7BQZN","short_pith_number":"pith:ASBIBJGZ","canonical_record":{"source":{"id":"1203.3503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-15T11:17:56Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"a205e5b9e4d209282169fbb8247f1b2a48f5dd82bfa50a3827bc24c86212721d","abstract_canon_sha256":"5864fe3389a1968b097da22c768c86555f843ecfe141d4cbca01bccbc6c6fd7e"},"schema_version":"1.0"},"canonical_sha256":"048280a4d96d2c69c289fe9d987c30cb788e361f8589017c42a4de21b8a35d62","source":{"kind":"arxiv","id":"1203.3503","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3503","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3503v1","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3503","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"ASBIBJGZNUWG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASBIBJGZNUWGTQUJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASBIBJGZ","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ASBIBJGZNUWGTQUJ72OZQ7BQZN","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-15T11:17:56Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"a205e5b9e4d209282169fbb8247f1b2a48f5dd82bfa50a3827bc24c86212721d","abstract_canon_sha256":"5864fe3389a1968b097da22c768c86555f843ecfe141d4cbca01bccbc6c6fd7e"},"schema_version":"1.0"},"canonical_sha256":"048280a4d96d2c69c289fe9d987c30cb788e361f8589017c42a4de21b8a35d62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:00.162224Z","signature_b64":"5Xm9Ba8D99ZgdzkNhCNddjMZz5VkGJpEsRnQ2Wpfczec/yTbQRqWLge2m2mJz38pfk1RcuEcxOpytzF4bLmCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048280a4d96d2c69c289fe9d987c30cb788e361f8589017c42a4de21b8a35d62","last_reissued_at":"2026-05-18T04:00:00.161386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:00.161386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3503","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":"2026-05-18T04:00:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ljki/Mu5LoJJeBOFJLt0TbSaWduDoMqq6ZN7u5MyyOQxcs4PVm2RsHlrs3vICb7etR3zvbmsVZKl75qI4e35Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T13:41:43.042085Z"},"content_sha256":"4a4a79a8234147e5d34c24d318193856d8f8a1da566a377d08d4542fd9431458","schema_version":"1.0","event_id":"sha256:4a4a79a8234147e5d34c24d318193856d8f8a1da566a377d08d4542fd9431458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ASBIBJGZNUWGTQUJ72OZQ7BQZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Class of Bias-Amplifying Variables that Endanger Effect Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"stat.ME","authors_text":"Judea Pearl","submitted_at":"2012-03-15T11:17:56Z","abstract_excerpt":"This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: 1. the bias-amplifying potential of instrumental variables extends over to non-linear models, though not as swee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3503","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":"2026-05-18T04:00:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUVNs5g6D6Ay3VsKq4dBWx8tMSCr5Qv0qOxrKdYltZ1jxfq1AF0KNyE8hrfqpuFDKsO/ut0BpTdwgzxFRLJFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T13:41:43.042555Z"},"content_sha256":"b675945b7bd13b7b21863401a1dde2c54d8094588c5156e4dd2dcb4e18462d4d","schema_version":"1.0","event_id":"sha256:b675945b7bd13b7b21863401a1dde2c54d8094588c5156e4dd2dcb4e18462d4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/bundle.json","state_url":"https://pith.science/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/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":"2026-08-23T13:41:43Z","links":{"resolver":"https://pith.science/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN","bundle":"https://pith.science/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/bundle.json","state":"https://pith.science/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASBIBJGZNUWGTQUJ72OZQ7BQZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ASBIBJGZNUWGTQUJ72OZQ7BQZN","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":"5864fe3389a1968b097da22c768c86555f843ecfe141d4cbca01bccbc6c6fd7e","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-15T11:17:56Z","title_canon_sha256":"a205e5b9e4d209282169fbb8247f1b2a48f5dd82bfa50a3827bc24c86212721d"},"schema_version":"1.0","source":{"id":"1203.3503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3503","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3503v1","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3503","created_at":"2026-05-18T04:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"ASBIBJGZNUWG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASBIBJGZNUWGTQUJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASBIBJGZ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:b675945b7bd13b7b21863401a1dde2c54d8094588c5156e4dd2dcb4e18462d4d","target":"graph","created_at":"2026-05-18T04:00:00Z","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 note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: 1. the bias-amplifying potential of instrumental variables extends over to non-linear models, though not as swee","authors_text":"Judea Pearl","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-15T11:17:56Z","title":"On a Class of Bias-Amplifying Variables that Endanger Effect Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3503","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":"sha256:4a4a79a8234147e5d34c24d318193856d8f8a1da566a377d08d4542fd9431458","target":"record","created_at":"2026-05-18T04:00:00Z","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":"5864fe3389a1968b097da22c768c86555f843ecfe141d4cbca01bccbc6c6fd7e","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-15T11:17:56Z","title_canon_sha256":"a205e5b9e4d209282169fbb8247f1b2a48f5dd82bfa50a3827bc24c86212721d"},"schema_version":"1.0","source":{"id":"1203.3503","kind":"arxiv","version":1}},"canonical_sha256":"048280a4d96d2c69c289fe9d987c30cb788e361f8589017c42a4de21b8a35d62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"048280a4d96d2c69c289fe9d987c30cb788e361f8589017c42a4de21b8a35d62","first_computed_at":"2026-05-18T04:00:00.161386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:00.161386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Xm9Ba8D99ZgdzkNhCNddjMZz5VkGJpEsRnQ2Wpfczec/yTbQRqWLge2m2mJz38pfk1RcuEcxOpytzF4bLmCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:00.162224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a4a79a8234147e5d34c24d318193856d8f8a1da566a377d08d4542fd9431458","sha256:b675945b7bd13b7b21863401a1dde2c54d8094588c5156e4dd2dcb4e18462d4d"],"state_sha256":"92cd2f2984a526c1927829152fa63912cd6f1b28b1703a43447504ad901374c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lc5UUYYJaVOG7l5zb3wJ89FoVn5mqfrqbgXXX4mMNnOT8J8OUE2dWfu2T7yXqxTcdTvoeWjRNF+J9UO8iRimBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T13:41:43.049545Z","bundle_sha256":"6c5822b1f399ef5ed68098adaa8be76aeb8e2c99dd9695cb22d68cd8dd6f9d2b"}}