Certified-Robustness Evaluation for Computer Agriculture Weed-Detection Models Under Variable Spray-Nozzle Geometry: An Artificial Intelligence Randomized-Smoothing Guarantee for Herbicide-Dose Safety

Weed-detection classifiers that drive variable-rate herbicide sprayers must remain reliable when nozzle geometry, spray angle and boom height perturb the images they receive, yet conventional accuracy metrics say nothing about the worst-case perturbation a deployed model can survive. The argument proceeds in three formal steps. First, a nozzle-geometry perturbation model is derived from the geometry of fan nozzles, boom height and forward speed, giving an explicit bound on the pixel displacement a classifier must tolerate. Second, a randomized-smoothing guarantee is stated and proved for the smoothed weed-detection classifier, yielding an L2 certified radius that is converted into a spray-overlap tolerance. Third, a dose-safety criterion is defined that maps certified radius to admissible herbicide application error, so that a certification failure is expressed in litres per hectare rather than in abstract distance. The framework is methodological and theoretical: no field trial is reported and no observational data are claimed. A design-analysis component characterises the operating characteristics of a before-after-control-impact evaluation of the certification procedure under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells; 56 clusters are required for 5 percentage points at 80% power. The contribution is a chain from nozzle geometry through certified radius to dose error, which converts an abstract robustness certificate into an auditable spray-safety statement.