Evaluation of Integrated-Gradient Path-Completeness Audits for Computer Vision Agriculture Disease Classifiers Under Shadowed Canopy Illumination: An Interpretability Completeness Bound for Smallholder Fungicide Triage

Integrated gradients (IG) is widely used to attribute the decisions of convolutional disease classifiers to image regions, yet its completeness axiom is stated for differentiable functions on continuous inputs and says nothing about the discrete, shadow-dominated imagery that smallholder triage systems actually receive. the present analysis treats IG path-completeness as an auditable property of a deployed classifier and derives a bound on the completeness residual that a shadowed-canopy image can be expected to produce. The classifier is modelled as a composition of a locally affine feature map and a Lipschitz decision head, and the shadow field is modelled as a multiplicative illumination factor bounded below by a canopy attenuation floor. Under these assumptions the completeness residual is bounded by a term proportional to the attenuation floor, the Lipschitz constant of the head, and the path length in input space, plus a discretisation term from the Riemann approximation of the path integral. The bound is stated as Theorem 3.1, with a corollary giving the shadow depth at which the residual exceeds a triage-relevant tolerance, and a further corollary giving the number of path steps needed to keep discretisation error below that tolerance. The result reframes IG completeness from a property that holds in the limit to a budget that a deployment either meets or does not, and it identifies the shadow attenuation floor, not the attribution algorithm, as the quantity that smallholder triage pipelines must measure before IG maps are shown to extension workers.