Evaluation of Counterfactual Explanation Reachability for Artificial Intelligence Agriculture Nitrogen-Recommendation Models Under Water-Boundary Constraints: An Interpretability Actionability Bound for Smallholder Input Cost

Counterfactual explanations for nitrogen-recommendation models promise smallholders an actionable route from an unfavourable recommendation to a better one, but that promise is void when the recommended change lies outside the farmer's feasible set. the present analysis formalises counterfactual reachability under water-boundary constraints and derives an interpretability actionability bound: the probability that a counterfactual generated for a nitrogen model is implementable by a water-constrained smallholder. The bound is expressed as a function of the feasible-set geometry, the model's local response surface and the counterfactual generation tolerance, and it is shown to collapse to a simple threshold condition when the water constraint is binding. A design-based evaluation of the before-after-control-impact estimator used to audit such models is reported, with a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64; power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required for 80 per cent power at a 5 percentage point effect. The contribution is a formal criterion that separates counterfactual plausibility from counterfactual actionability, together with the design parameters needed to audit nitrogen recommenders for smallholder input cost.