{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4MU7PMW7YF2B5A5SC322L44J76","short_pith_number":"pith:4MU7PMW7","canonical_record":{"source":{"id":"1602.01196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-03T05:56:30Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"0e826fa978145baa4c9a3bcaad796c2a74fccd7488e6428f6ec3f25012169c82","abstract_canon_sha256":"51dbfbe49a4fa587e3c12af3fc29d3325b27dbfe9b22e59ed3470fbc3d360d92"},"schema_version":"1.0"},"canonical_sha256":"e329f7b2dfc1741e83b216f5a5f389ff97db9cfe06f3e36101889e194a1b1f8b","source":{"kind":"arxiv","id":"1602.01196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01196","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01196v1","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01196","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"4MU7PMW7YF2B","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4MU7PMW7YF2B5A5S","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4MU7PMW7","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4MU7PMW7YF2B5A5SC322L44J76","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-03T05:56:30Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"0e826fa978145baa4c9a3bcaad796c2a74fccd7488e6428f6ec3f25012169c82","abstract_canon_sha256":"51dbfbe49a4fa587e3c12af3fc29d3325b27dbfe9b22e59ed3470fbc3d360d92"},"schema_version":"1.0"},"canonical_sha256":"e329f7b2dfc1741e83b216f5a5f389ff97db9cfe06f3e36101889e194a1b1f8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:20.849105Z","signature_b64":"yIyOSPGNhDWMOUCEN1is6hJ/BVMNKFo3UObYPEzskwy+Cb8Og5sDPHhMvVg8ACm9cbUQr5/a0kr9LnAB9ZS4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e329f7b2dfc1741e83b216f5a5f389ff97db9cfe06f3e36101889e194a1b1f8b","last_reissued_at":"2026-05-18T01:21:20.848509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:20.848509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01196","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":"2026-05-18T01:21:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmiaXHMbfgeGJlbov/WyGszcsKZ/f0bHnXY/D4cIC4ACqrRaVs6dy86qrbyrE4s/rMTpNYoIKwi5cNcV6Lb9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:05:53.102347Z"},"content_sha256":"ddfb63a98af97e9ff550ece216bdfae2b1a257a3d23ca814cb08fb3339c0b7c2","schema_version":"1.0","event_id":"sha256:ddfb63a98af97e9ff550ece216bdfae2b1a257a3d23ca814cb08fb3339c0b7c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4MU7PMW7YF2B5A5SC322L44J76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Principal stratification analysis using principal scores","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Jiannan Lu, Peng Ding","submitted_at":"2016-02-03T05:56:30Z","abstract_excerpt":"Practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. However, in many cases we cannot randomize the intermediate variable, resulting in sample selection problems even in randomized experiments. Therefore, we view randomized experiments with intermediate variables as semi-observational studies. In parallel with the analysis of observational studies, we provide a theoretical foundation for conducting objective causal inference with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01196","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":"2026-05-18T01:21:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LjYMuhG9kid2zN3nwNnJD7KaSw6hdrFyLhomipB5aluTJwFiWtRsgGQRDgWcKujLMZS8eFutdcjdn61MwA2XDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:05:53.102691Z"},"content_sha256":"b7946d2da0b253dc861c2e593a471e739ed84b357e1eb00b5d238d8628e7b7f0","schema_version":"1.0","event_id":"sha256:b7946d2da0b253dc861c2e593a471e739ed84b357e1eb00b5d238d8628e7b7f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MU7PMW7YF2B5A5SC322L44J76/bundle.json","state_url":"https://pith.science/pith/4MU7PMW7YF2B5A5SC322L44J76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MU7PMW7YF2B5A5SC322L44J76/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":"2026-07-04T22:05:53Z","links":{"resolver":"https://pith.science/pith/4MU7PMW7YF2B5A5SC322L44J76","bundle":"https://pith.science/pith/4MU7PMW7YF2B5A5SC322L44J76/bundle.json","state":"https://pith.science/pith/4MU7PMW7YF2B5A5SC322L44J76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MU7PMW7YF2B5A5SC322L44J76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4MU7PMW7YF2B5A5SC322L44J76","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":"51dbfbe49a4fa587e3c12af3fc29d3325b27dbfe9b22e59ed3470fbc3d360d92","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-03T05:56:30Z","title_canon_sha256":"0e826fa978145baa4c9a3bcaad796c2a74fccd7488e6428f6ec3f25012169c82"},"schema_version":"1.0","source":{"id":"1602.01196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01196","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01196v1","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01196","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"4MU7PMW7YF2B","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4MU7PMW7YF2B5A5S","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4MU7PMW7","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b7946d2da0b253dc861c2e593a471e739ed84b357e1eb00b5d238d8628e7b7f0","target":"graph","created_at":"2026-05-18T01:21:20Z","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":"Practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. However, in many cases we cannot randomize the intermediate variable, resulting in sample selection problems even in randomized experiments. Therefore, we view randomized experiments with intermediate variables as semi-observational studies. In parallel with the analysis of observational studies, we provide a theoretical foundation for conducting objective causal inference with ","authors_text":"Jiannan Lu, Peng Ding","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-03T05:56:30Z","title":"Principal stratification analysis using principal scores"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01196","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:ddfb63a98af97e9ff550ece216bdfae2b1a257a3d23ca814cb08fb3339c0b7c2","target":"record","created_at":"2026-05-18T01:21:20Z","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":"51dbfbe49a4fa587e3c12af3fc29d3325b27dbfe9b22e59ed3470fbc3d360d92","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-03T05:56:30Z","title_canon_sha256":"0e826fa978145baa4c9a3bcaad796c2a74fccd7488e6428f6ec3f25012169c82"},"schema_version":"1.0","source":{"id":"1602.01196","kind":"arxiv","version":1}},"canonical_sha256":"e329f7b2dfc1741e83b216f5a5f389ff97db9cfe06f3e36101889e194a1b1f8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e329f7b2dfc1741e83b216f5a5f389ff97db9cfe06f3e36101889e194a1b1f8b","first_computed_at":"2026-05-18T01:21:20.848509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:20.848509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yIyOSPGNhDWMOUCEN1is6hJ/BVMNKFo3UObYPEzskwy+Cb8Og5sDPHhMvVg8ACm9cbUQr5/a0kr9LnAB9ZS4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:20.849105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddfb63a98af97e9ff550ece216bdfae2b1a257a3d23ca814cb08fb3339c0b7c2","sha256:b7946d2da0b253dc861c2e593a471e739ed84b357e1eb00b5d238d8628e7b7f0"],"state_sha256":"e5eada21b79b5f5d6cdcd65b96de962f77a642aaef85bdca2954d2733e0e13c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+lA64chsmorLMdKSOGSwYODaKdGJMHF6ahpM+BXarGNThHH9TMglCLrn35CERl04bFsTituCajH8UH+UJ7FAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:05:53.104584Z","bundle_sha256":"cd005a78a08ccc35442d30a92be306b09a8626b44120bc3bee06755b797aba2c"}}