Operational-Shape Reduction Across Operating Regimes of Quantum-Chaos Models — QOR, Non-Redundant Differences, Directional Substitutability, and Interval Dependence

This paper develops a method for reducing families of quantum-chaos models by identifying which differences remain operationally non-redundant across changing regimes. Rather than treating formal distinctions between models as sufficient for establishing physical or explanatory difference, the analysis asks whether those distinctions alter prediction, intervention, control, observability, noise robustness, experimental reconstruction, or computational cost under specified operating conditions. The paper introduces Quantum Operational Reduction (QOR) as a framework for comparing models across regimes and testing directional substitutability: whether one model can replace another for a given task, scale, noise level, temporal window, or observational configuration without loss of relevant performance. The resulting equivalence relations are therefore interval-dependent and need not be symmetric. A model may substitute for another within one operational interval while failing outside it or in the reverse direction. The analysis distinguishes formal non-identity from operational non-redundancy and uses quantum-chaos models as a test case for determining which structural differences survive empirical, computational, and control-oriented comparison. The broader claim is that model plurality should be evaluated not only by mathematical representation or interpretation, but by the regime-specific differences that actually change reachable predictions, interventions, and experimental outcomes.