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We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model.","weakest_assumption":"The CATE function is identifiable from observed data under randomized treatment assignment, allowing the sublevel-set probabilities to be targeted and estimated via monotone function techniques combined with machine learning, as used in the numerical studies based on synthesized randomized trial data."}},"verdict_id":"d17e324e-ea83-4eb8-b14d-e702e3d1769a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f9092720eea5da7fdb420f31e68df1a3fd0f98a8dcace46c47eba67e3f3b187c","target":"record","created_at":"2026-05-20T00:00:55Z","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":"cecc431fb007406f9897ace16ef658ac8a3f341c383f73d4950587ef5c5f8205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-05-14T20:01:21Z","title_canon_sha256":"31486c61816a560bc6952bfaf978eb18ed15e3116ed6aa91c5ab60e54f8ef541"},"schema_version":"1.0","source":{"id":"2605.15373","kind":"arxiv","version":1}},"canonical_sha256":"b1a29b8510135312c43bbf75c04a44114d27d3d22a66b2392c92a6aaa480b12d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1a29b8510135312c43bbf75c04a44114d27d3d22a66b2392c92a6aaa480b12d","first_computed_at":"2026-05-20T00:00:55.114656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:55.114656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"atZL0Lwe05lSDmUz5G51Tu9fVFCdJcduBv++dBp4TLvrfDdY64x5mHJNAaxfiI6v4PBOELkOaUK/POMT0QsBDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:55.115578Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9092720eea5da7fdb420f31e68df1a3fd0f98a8dcace46c47eba67e3f3b187c","sha256:3d76b09eab30a52d74353a858a7be431165d2ddace435633fab79976d21dd5bb"],"state_sha256":"9906381b061e4869aca575a96386393ebf492fc9c2126174f6eb3c32277f138b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyyfDhQ9VeiEVGy3M/NqGnK+BmLjHarRb3DtOrTiWKKOs/Uy8OiXp+r8Ep6MZsfImR7gsLi7vhxESZMMcsdDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T09:34:02.867659Z","bundle_sha256":"96b24b0961c7a51eede91430c6464519d3f1e48633cfaa4d7c8bd9b911acca38"}}