{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E36VJRLXWJGJGTRVDH3KP6WA2X","short_pith_number":"pith:E36VJRLX","canonical_record":{"source":{"id":"1811.10223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-11-26T08:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"1dea77796d5d295fad5d95c0ca3b21314cbfe358531954e9cd2782b49988055f","abstract_canon_sha256":"1977d0f11b26af8229810de2f3c476b4c1ce43b515b31aa8bb45281874f4c3d9"},"schema_version":"1.0"},"canonical_sha256":"26fd54c577b24c934e3519f6a7fac0d5d24c134e499724333c83f2864ef12bad","source":{"kind":"arxiv","id":"1811.10223","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10223","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10223v2","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10223","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"E36VJRLXWJGJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E36VJRLXWJGJGTRV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E36VJRLX","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E36VJRLXWJGJGTRVDH3KP6WA2X","target":"record","payload":{"canonical_record":{"source":{"id":"1811.10223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-11-26T08:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"1dea77796d5d295fad5d95c0ca3b21314cbfe358531954e9cd2782b49988055f","abstract_canon_sha256":"1977d0f11b26af8229810de2f3c476b4c1ce43b515b31aa8bb45281874f4c3d9"},"schema_version":"1.0"},"canonical_sha256":"26fd54c577b24c934e3519f6a7fac0d5d24c134e499724333c83f2864ef12bad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:35.978346Z","signature_b64":"JwLDczfDtzuI/uCaUmlfkIkqSP0SIQuLdnKSBxZk6UaPhKOpl1pO/wmS3NyrqGBY6utjt8UZq8O34SlTLX8KDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26fd54c577b24c934e3519f6a7fac0d5d24c134e499724333c83f2864ef12bad","last_reissued_at":"2026-05-17T23:47:35.977869Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:35.977869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.10223","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":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eepFkEkyeuONVURYu+j1tEXdjoMi14Odwht9Am74/9/7Y8xr4ziivytr9gVxC4F/cViNH5vrIv8xypUDxPcCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:02:39.671991Z"},"content_sha256":"5f2cc256f4d1487c68541f9268e175616ae0b5fdb0140e5c30919065100b4568","schema_version":"1.0","event_id":"sha256:5f2cc256f4d1487c68541f9268e175616ae0b5fdb0140e5c30919065100b4568"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E36VJRLXWJGJGTRVDH3KP6WA2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian Weighted Mendelian Randomization for Causal Inference based on Summary Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Can Yang, Gang Chen, Jia Zhao, Jingsi Ming, Jin Liu, Xianghong Hu","submitted_at":"2018-11-26T08:01:26Z","abstract_excerpt":"The results from Genome-Wide Association Studies (GWAS) on thousands of phenotypes provide an unprecedented opportunity to infer the causal effect of one phenotype (exposure) on another (outcome). Mendelian randomization (MR), an instrumental variable (IV) method, has been introduced for causal inference using GWAS data. Due to the polygenic architecture of complex traits/diseases and the ubiquity of pleiotropy, however, MR has many unique challenges compared to conventional IV methods. We propose a Bayesian weighted Mendelian randomization (BWMR) for causal inference to address these challeng"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10223","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":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDNg0g+2ZENLlhj6szRqsodyGAMG7vyPOEHiAQl/M6CjR0kOXLRvy357JwesLEm+Jz8qwRnSRHk+dp/OWJomAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:02:39.672633Z"},"content_sha256":"69ac48d9bfac2fde54e165d238a1733fedf1587050c3bea1ff693ec8721fcedc","schema_version":"1.0","event_id":"sha256:69ac48d9bfac2fde54e165d238a1733fedf1587050c3bea1ff693ec8721fcedc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/bundle.json","state_url":"https://pith.science/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/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":"2026-05-31T01:02:39Z","links":{"resolver":"https://pith.science/pith/E36VJRLXWJGJGTRVDH3KP6WA2X","bundle":"https://pith.science/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/bundle.json","state":"https://pith.science/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E36VJRLXWJGJGTRVDH3KP6WA2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E36VJRLXWJGJGTRVDH3KP6WA2X","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":"1977d0f11b26af8229810de2f3c476b4c1ce43b515b31aa8bb45281874f4c3d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-11-26T08:01:26Z","title_canon_sha256":"1dea77796d5d295fad5d95c0ca3b21314cbfe358531954e9cd2782b49988055f"},"schema_version":"1.0","source":{"id":"1811.10223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10223","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10223v2","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10223","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"E36VJRLXWJGJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E36VJRLXWJGJGTRV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E36VJRLX","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:69ac48d9bfac2fde54e165d238a1733fedf1587050c3bea1ff693ec8721fcedc","target":"graph","created_at":"2026-05-17T23:47:35Z","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":"The results from Genome-Wide Association Studies (GWAS) on thousands of phenotypes provide an unprecedented opportunity to infer the causal effect of one phenotype (exposure) on another (outcome). Mendelian randomization (MR), an instrumental variable (IV) method, has been introduced for causal inference using GWAS data. Due to the polygenic architecture of complex traits/diseases and the ubiquity of pleiotropy, however, MR has many unique challenges compared to conventional IV methods. We propose a Bayesian weighted Mendelian randomization (BWMR) for causal inference to address these challeng","authors_text":"Can Yang, Gang Chen, Jia Zhao, Jingsi Ming, Jin Liu, Xianghong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-11-26T08:01:26Z","title":"Bayesian Weighted Mendelian Randomization for Causal Inference based on Summary Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10223","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":"sha256:5f2cc256f4d1487c68541f9268e175616ae0b5fdb0140e5c30919065100b4568","target":"record","created_at":"2026-05-17T23:47:35Z","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":"1977d0f11b26af8229810de2f3c476b4c1ce43b515b31aa8bb45281874f4c3d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-11-26T08:01:26Z","title_canon_sha256":"1dea77796d5d295fad5d95c0ca3b21314cbfe358531954e9cd2782b49988055f"},"schema_version":"1.0","source":{"id":"1811.10223","kind":"arxiv","version":2}},"canonical_sha256":"26fd54c577b24c934e3519f6a7fac0d5d24c134e499724333c83f2864ef12bad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26fd54c577b24c934e3519f6a7fac0d5d24c134e499724333c83f2864ef12bad","first_computed_at":"2026-05-17T23:47:35.977869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:35.977869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JwLDczfDtzuI/uCaUmlfkIkqSP0SIQuLdnKSBxZk6UaPhKOpl1pO/wmS3NyrqGBY6utjt8UZq8O34SlTLX8KDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:35.978346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f2cc256f4d1487c68541f9268e175616ae0b5fdb0140e5c30919065100b4568","sha256:69ac48d9bfac2fde54e165d238a1733fedf1587050c3bea1ff693ec8721fcedc"],"state_sha256":"e021f7449de83685837de768b4092e2b8f9d9cfe1c60939d8cd7bb250acf6be1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/uVTp0/qt1yBBDg9qp5NHweNO800zBikt7e6SOy333h3bxnZJGeJhdxKAU+eEqhOYRSIdm7JcsClkHwaBxWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:02:39.675614Z","bundle_sha256":"341f7f34ed1af12ab1fe223cd0a2c743c502d4d5b1eea9ed17a0da6a598d0634"}}