SpectralGuard: a Spectrally grounded λ-SHAP framework for XAI validity certification in pharmaceutical supply chain networks

Permutation-based explainability methods such as SHAP are central to regulatory compliance in AI-governed pharmaceutical supply chains across Sub-Saharan Africa, yet their validity depends on a structural property that existing frameworks do not monitor: the algebraic connectivity of the supply hypergraph, quantified by the Fiedler eigenvalue λ 2 . We prove that λ 2 → 0 is a sufficient condition for permutation-based XAI failure (Theorem 3.5): no increase in sampling effort can recover validity once network connectivity collapses. We introduce SpectralGuard, demonstrated on a calibrated synthetic DGP driven by real Eskom load-shedding and SARB ZAR/USD records ( n = 3, 227 business days, 2014–2026); all spectral results are from the synthetic hypergraph. λ-SHAP shrinks attributions toward a fluid-regime prior using λ 2 ( t ) as the shrinkage weight, maintaining auditability at an explicit bias–variance cost (Remark 3.12). A probabilistic validity certificate V ( t ) combines four spectral metrics with SHA-256 tamper-evidence. An oracle experiment ( B = 500, Seed = 2,026) demonstrates 70.4–89.2% attribution MSE reduction across governance regimes. The spectral gate is the decisive ablation component. In the synthetic DGP, early-warning detection leads classical baselines by 19 business days (λ c alert preceding the λ m crossing). Field validation on real CCMDD procurement data is planned for 2027 (PLMIF-2). A nine-step DHIS2 integration pathway supports SDG 3, 9, 13, and 16.