Admissible Transition Systems with Induced Geometry and Transparent Transition Readouts

This paper develops a structural framework for discrete decision systems in which admissible transitions define the induced geometry of observable processes. The framework introduces a neighborhood-free formulation that avoids predefined graph proximity and probabilistic assumptions. Instead, admissible transition structures are treated as the primary object from which notions of geometry, paths, costs, and observable behavior are induced. A transparent Markov-type readout is constructed directly from observed transitions, separating the structural layer from stochastic interpretation. The framework is applicable to discrete transition systems, automation, human-in-the-loop systems, and explainable AI settings.