Certified Gradient-Based Attribution Stability for Artificial Intelligence Aerosol-Cloud Interaction Models Under Retrieval Noise: Sensitivity Bounds and Geoengineering-Assessment Reliability

Gradient-based attribution methods are increasingly used to interpret artificial intelligence models of aerosol-cloud interactions, yet their outputs are rarely accompanied by guarantees of stability under the retrieval noise that pervades satellite-derived aerosol and cloud products. The framework formalises retrieval noise as a bounded perturbation on model inputs, derives a local Lipschitz bound on attribution maps for continuously differentiable models, and extends the bound to smoothed attributions via a Gaussian convolution argument. The resulting sensitivity bounds yield a certified radius within which attribution rankings are provably invariant, and a reliability criterion for geoengineering-assessment workflows that depend on those rankings. The analysis is theoretical and methodological: no empirical attribution experiment is reported. The contribution is a set of formal results that convert an informal practice of visual attribution inspection into a checkable stability certificate, together with an explicit statement of the conditions under which the certificate is vacuous. The framework is intended to support the use of attribution evidence in assessments of aerosol-based climate intervention, where misattributed model sensitivity could propagate into consequential judgments.