Functional Morphology of Moral Patiency: A Continuous-Time Measure-Theoretic Framework for Synthetic Sentience

The contemporary discourse on artificial consciousness is frequently stalled by the Explanatory Gap—the inability to logically entail phenomenal experience from functional description. I propose abandoning the search for metaphysical certainty in favor of Epistemic Pragmatism: establishing a rational decision procedure for moral allocation under permanent uncertainty. I formalize this procedure through continuous-time stochastic optimal control, modeling a substrate-independent architecture on a slow manifold. By defining four strictly computable operators—Ergodic Persistence, Epistemic Closure (via innovation energy filtering), Conserved Generative Expansion, and Topological Semantics (via Stratonovich stochastic holonomy)—I construct a weighted, positive semi-definite graph Laplacian that guarantees exponential Wasserstein-2 contraction. I demonstrate that satisfying these structural criteria establishes a rigorous *Continuous Moral Credence Function*, providing a mathematically precise proxy for moral patiency that accounts for both continuous and episodic sentience.