{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I3L4DNJYDSFNWL2TVEIORT2HA2","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":"4ad46a85f2df73141d075a371f179c217149d6fb7deacf0593bfbae4100e6e26","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-09-13T17:33:39Z","title_canon_sha256":"42b7c86996eb5d6616e7f31335d8631062926bf9d48ff45291938077efd51b3b"},"schema_version":"1.0","source":{"id":"2509.10916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.10916","created_at":"2026-07-05T12:11:30Z"},{"alias_kind":"arxiv_version","alias_value":"2509.10916v1","created_at":"2026-07-05T12:11:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.10916","created_at":"2026-07-05T12:11:30Z"},{"alias_kind":"pith_short_12","alias_value":"I3L4DNJYDSFN","created_at":"2026-07-05T12:11:30Z"},{"alias_kind":"pith_short_16","alias_value":"I3L4DNJYDSFNWL2T","created_at":"2026-07-05T12:11:30Z"},{"alias_kind":"pith_short_8","alias_value":"I3L4DNJY","created_at":"2026-07-05T12:11:30Z"}],"graph_snapshots":[{"event_id":"sha256:a04f567bd2558b5a178cc39159e9ef1e74590f20d77740ce3a3094b96046c794","target":"graph","created_at":"2026-07-05T12:11:30Z","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/2509.10916/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Causal mediation analysis is a powerful tool in environmental health research, allowing researchers to uncover the pathways through which exposures influence health outcomes. While traditional mediation methods have been widely applied to individual exposures, real-world scenarios often involve complex mixtures. Such mixtures introduce unique methodological challenges, including multicollinearity, sparsity of active exposures, and potential nonlinear and interactive effects. This paper provides an overview of several commonly used approaches for mediation analysis under exposure mixture settin","authors_text":"Bhramar Mukherjee, John D. Meeker, Joshua L. Warren, Sean McGrath, Sung Kyun Park, Yiran Wang, Yi-Ting Lin","cross_cats":["stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-09-13T17:33:39Z","title":"A Tutorial on Conducting Mediation Analysis with Exposure Mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10916","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:af5d836bde88fc990182a3f9f6fd6791c627973e425e8aacad509dfa009ea82f","target":"record","created_at":"2026-07-05T12:11:30Z","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":"4ad46a85f2df73141d075a371f179c217149d6fb7deacf0593bfbae4100e6e26","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-09-13T17:33:39Z","title_canon_sha256":"42b7c86996eb5d6616e7f31335d8631062926bf9d48ff45291938077efd51b3b"},"schema_version":"1.0","source":{"id":"2509.10916","kind":"arxiv","version":1}},"canonical_sha256":"46d7c1b5381c8adb2f53a910e8cf4706bbe0beb79ca5924ef694e9a41e649b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46d7c1b5381c8adb2f53a910e8cf4706bbe0beb79ca5924ef694e9a41e649b38","first_computed_at":"2026-07-05T12:11:30.360285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:11:30.360285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jaivada2PXxSxs7U6l9masJuz4fX+GMr9xO92MhrcBkM+M8vFDO2Cd65jLeZqGjhn3AsT0tgroEvsrrds7sECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:11:30.360711Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.10916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af5d836bde88fc990182a3f9f6fd6791c627973e425e8aacad509dfa009ea82f","sha256:a04f567bd2558b5a178cc39159e9ef1e74590f20d77740ce3a3094b96046c794"],"state_sha256":"2491f6ecb95d8d099a12dc0ad2ef4587a3ddf0997bf4fa2b0548dde2d19f1148"}