Selective-Prediction Evaluation for Computer Agriculture Fertilizer Advisories Under Soil-Test Sampling Gaps: An Artificial Intelligence Abstention-Risk Bound for Over-Application Safety

Fertilizer advisory systems built on machine learning must issue a recommendation for every field, yet soil-test sampling gaps mean that many fields arrive with covariates that are only partially observed. The framework treats abstention as a first-class output, defines the abstention-risk profile as the conditional over-application rate among retained cases, and proves that under a bounded calibration gap the profile is controlled by the abstention threshold and the sampling-gap severity. A design-based evaluation is characterised under a declared variance structure with between-cluster SD 6.0, residual SD 4.5 and intraclass correlation 0.64; power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design requires 52 clusters to detect a 5 percentage-point effect at 80% power. The bound converts an evaluation target into an auditable abstention rule, and the paper argues that advisory evaluations should report abstention-risk profiles alongside aggregate accuracy.