A Unified Discrete Mathematical Framework for Validation and Feature Attribution of Trust in Hybrid AI-Driven Network Architectures

Abstract

This paper introduces a discrete mathematical framework that renders the trustworthiness of automated nodes in hybrid AI-driven networks both cryptographically verifiable and mathematically provable. The framework is built on a bounded lattice of admissible node states, normalized feature attributions, and trust valuations, enabling the definition of performance metrics and composite trust functionals. Formal proofs establish boundedness, monotonicity, and stability, ensuring that node rankings form a well-defined total preorder resilient to input perturbations. Cryptographic validation is achieved through a SHA 256 attestation pipeline, providing digest generation, hash chaining, and tamper-resistance under collision-resistance assumptions. Interpretability is integrated via Shapley-value feature attribution, formulated as an additive set function on the Boolean lattice of feature coalitions, linking explainable AI directly to discrete algebra. A hybrid BiLSTM–BiGRU sequence model with attention serves as the predictive engine, improving forecasting accuracy by 2–4% over baselines, with statistical significance confirmed by Wilcoxon signed-rank testing. The contribution is a unified, mathematically rigorous pipeline that combines discrete trust modeling, cryptographic attestation, and explainable AI, supported by complete theorems and proofs for secure, interpretable, and adaptive network management.