This paper starts from two fundamental physical principles—Information Conservation and Finite-Step Computability—to argue that key classifications in modeltheory, such as stability, NIP (No Independence Property), and o-minimal structures, are not merely artificial logical divisions but direct mathematical manifestations of the intrinsic requirements of observability and simulability in the physicalworld. The research demonstrates that information conservation excludes the possibility of infinite branching of information in formal languages, thereby forcingtheories to possess stability. Finite-step computability requires a uniform upperbound on the complexity of definable sets, naturally leading to NIP properties andfinite VC dimension, and guiding towards the regular geometry described by ominimal structures. This paper further proposes quantitative experimental testsfor the emergent stability theory by analyzing the morphology of the power spectrum of cosmic large-scale structures and the growth trend of the VC dimensionof measurement events in quantum many-body systems. This establishes a falsifiable bridge between the “well-behaved” classifications in mathematical logic andthe “detectable” structures of the physical world.