{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EEXULWIQMHVY7PINV4UX7RBOUF","short_pith_number":"pith:EEXULWIQ","canonical_record":{"source":{"id":"2607.16086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-17T16:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"dcfbff5cea256222880e5dbcb338f9dbeea63f429a97f8697a491c66eedc876d","abstract_canon_sha256":"824da251e13576442eb97835c3c0abca9b0b1a6f4ae2580370fd634850c25104"},"schema_version":"1.0"},"canonical_sha256":"212f45d91061eb8fbd0daf297fc42ea17f77acd34d54427175addb79956e2b21","source":{"kind":"arxiv","id":"2607.16086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16086","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16086v1","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16086","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"EEXULWIQMHVY","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_16","alias_value":"EEXULWIQMHVY7PIN","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_8","alias_value":"EEXULWIQ","created_at":"2026-07-20T02:19:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EEXULWIQMHVY7PINV4UX7RBOUF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-17T16:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"dcfbff5cea256222880e5dbcb338f9dbeea63f429a97f8697a491c66eedc876d","abstract_canon_sha256":"824da251e13576442eb97835c3c0abca9b0b1a6f4ae2580370fd634850c25104"},"schema_version":"1.0"},"canonical_sha256":"212f45d91061eb8fbd0daf297fc42ea17f77acd34d54427175addb79956e2b21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T02:19:30.201188Z","signature_b64":"1Ye6SWVYTxdngjhR1Kg6SgOvu7ExWvOc2wSiM5RbbWDjCbAbn99h9ZraM8IIy61NxjP5xNR4ci0nwz14uQH1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"212f45d91061eb8fbd0daf297fc42ea17f77acd34d54427175addb79956e2b21","last_reissued_at":"2026-07-20T02:19:30.200357Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T02:19:30.200357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16086","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":"2026-07-20T02:19:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYRLDKfUubXPHjnKo7dZ6M2S/BRTSMg8o0Rncaif4nSRGNocz40OPdDJaDGvaUmFEryh6Oh9iJPn7aZ5lhd+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:04:39.212727Z"},"content_sha256":"6f4b221a0f313453065586dbc714155d935e030fc4cf579dee0ef1dcf4f858a1","schema_version":"1.0","event_id":"sha256:6f4b221a0f313453065586dbc714155d935e030fc4cf579dee0ef1dcf4f858a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EEXULWIQMHVY7PINV4UX7RBOUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improving Mendelian Randomization Analysis by Instrument Borrowing from Auxiliary Outcome Traits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anagh Chattopadhyay, Nilanjan Chatterjee","submitted_at":"2026-07-17T16:15:57Z","abstract_excerpt":"Mendelian randomization (MR) is a widely used approach for inferring causal effects of exposures on outcomes using genetic variants as instrumental variables; however, existing methods remain vulnerable to bias and/or loss of power in the presence of invalid instruments. We hypothesize that closely related outcome traits are likely to have a large overlap in underlying valid instruments in relation to a given exposure and that instrument borrowing (IB) across such traits can therefore yield more robust MR inference. To operationalize this idea, we first introduce a novel coheterogeneity statis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16086","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16086/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-20T02:19:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkEVr3MIRlagPWzYSixruFX44JcfiUdvXh4kD7ZL7yMuSbRbLulO1pdS63vxNrFA8Uxj2/TMwV+GuyiciVbdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:04:39.213931Z"},"content_sha256":"f5a55d802ade40caa6a56d0074f04634f0dfd987d5e8257c148c0de2da6ea2c0","schema_version":"1.0","event_id":"sha256:f5a55d802ade40caa6a56d0074f04634f0dfd987d5e8257c148c0de2da6ea2c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EEXULWIQMHVY7PINV4UX7RBOUF/bundle.json","state_url":"https://pith.science/pith/EEXULWIQMHVY7PINV4UX7RBOUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EEXULWIQMHVY7PINV4UX7RBOUF/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":"2026-08-04T22:04:39Z","links":{"resolver":"https://pith.science/pith/EEXULWIQMHVY7PINV4UX7RBOUF","bundle":"https://pith.science/pith/EEXULWIQMHVY7PINV4UX7RBOUF/bundle.json","state":"https://pith.science/pith/EEXULWIQMHVY7PINV4UX7RBOUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EEXULWIQMHVY7PINV4UX7RBOUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EEXULWIQMHVY7PINV4UX7RBOUF","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":"824da251e13576442eb97835c3c0abca9b0b1a6f4ae2580370fd634850c25104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-17T16:15:57Z","title_canon_sha256":"dcfbff5cea256222880e5dbcb338f9dbeea63f429a97f8697a491c66eedc876d"},"schema_version":"1.0","source":{"id":"2607.16086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16086","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16086v1","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16086","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"EEXULWIQMHVY","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_16","alias_value":"EEXULWIQMHVY7PIN","created_at":"2026-07-20T02:19:30Z"},{"alias_kind":"pith_short_8","alias_value":"EEXULWIQ","created_at":"2026-07-20T02:19:30Z"}],"graph_snapshots":[{"event_id":"sha256:f5a55d802ade40caa6a56d0074f04634f0dfd987d5e8257c148c0de2da6ea2c0","target":"graph","created_at":"2026-07-20T02:19:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.16086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mendelian randomization (MR) is a widely used approach for inferring causal effects of exposures on outcomes using genetic variants as instrumental variables; however, existing methods remain vulnerable to bias and/or loss of power in the presence of invalid instruments. We hypothesize that closely related outcome traits are likely to have a large overlap in underlying valid instruments in relation to a given exposure and that instrument borrowing (IB) across such traits can therefore yield more robust MR inference. To operationalize this idea, we first introduce a novel coheterogeneity statis","authors_text":"Anagh Chattopadhyay, Nilanjan Chatterjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-17T16:15:57Z","title":"Improving Mendelian Randomization Analysis by Instrument Borrowing from Auxiliary Outcome Traits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16086","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":"sha256:6f4b221a0f313453065586dbc714155d935e030fc4cf579dee0ef1dcf4f858a1","target":"record","created_at":"2026-07-20T02:19:30Z","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":"824da251e13576442eb97835c3c0abca9b0b1a6f4ae2580370fd634850c25104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-17T16:15:57Z","title_canon_sha256":"dcfbff5cea256222880e5dbcb338f9dbeea63f429a97f8697a491c66eedc876d"},"schema_version":"1.0","source":{"id":"2607.16086","kind":"arxiv","version":1}},"canonical_sha256":"212f45d91061eb8fbd0daf297fc42ea17f77acd34d54427175addb79956e2b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"212f45d91061eb8fbd0daf297fc42ea17f77acd34d54427175addb79956e2b21","first_computed_at":"2026-07-20T02:19:30.200357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T02:19:30.200357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Ye6SWVYTxdngjhR1Kg6SgOvu7ExWvOc2wSiM5RbbWDjCbAbn99h9ZraM8IIy61NxjP5xNR4ci0nwz14uQH1Cw==","signature_status":"signed_v1","signed_at":"2026-07-20T02:19:30.201188Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f4b221a0f313453065586dbc714155d935e030fc4cf579dee0ef1dcf4f858a1","sha256:f5a55d802ade40caa6a56d0074f04634f0dfd987d5e8257c148c0de2da6ea2c0"],"state_sha256":"08e6258298adac7ab88e26f8ec2ef135910cf520da60192acd68d0ce1f20da34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8aUd/tpYrRlY8Yp+0jex3M8nkBeyWe7wh0FRk4rQrPGkcufLfvVYtABLBEw0psY0UTA1H51PeQhuZdynohUiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T22:04:39.221745Z","bundle_sha256":"0f4f03c04d51af17ef2e4df38c8817d5cf79a5ce7d907ba24ffe3d63762200d2"}}