Decidable By Construction: Design-Time Verification for Trustworthy AI

The article introduces a design-time verification framework for AI models that asserts correctness before training, leveraging properties expressible as constraints over finitely generated abelian groups $\mathbb{Z}^n$. This framework integrates a dimensional type system, a program hypergraph for geometric product sparsity, and an adaptive domain model architecture, enabling polynomial-time decidability for model stability and correctness. This approach significantly reduces verification overhead compared to contemporary methods, making it particularly relevant for high-stakes AI applications where reliability is critical.