Coupling-Aware Counterfactual Reasoning for Causal Artificial Intelligence: Identification, Learnability Limits, and Sharp Bounds with Finite-Sample Inference

Probabilities of benefit, probabilities of causation and the dispersion of individual effects depend on the joint law of potential outcomes, which interventional data do not fix. Building on Fréchet–Makarov and partial-identification results, we show that every coupling of the interventional laws is induced by an empirically equivalent structural causal model, characterize the feasible joint laws when observational and experimental data are combined, and restate the classical criterion that an expected cross-world score is learnable exactly when it is additively separable. We turn these facts into a coupling audit that reports sharp identification intervals, computed by linear programming, with projection confidence intervals that have finite-sample coverage and asymptotic Imbens–Manski intervals. Over all couplings, the sharp range of the probability that an individual benefits is twice as wide as the Gaussian-copula range; under empirically indistinguishable models, an independence plug-in estimator remains biased by up to 0.16; two public randomized trials yield informative but wide intervals. On a 240- item stress test, three open-source language models answered identified items almost perfectly and non-identified items never correctly. Core results are machine-checked in Lean 4. Conclusions are limited to finite or univariate outcomes, the stated model classes and, for the pilot, small models