Towards a Constraint-Based Framework for Physical Theories

We propose a preliminary mathematical framework for physical theories based on experimentally grounded constraints. A physical theory is represented as a structured object (S, O, D) consisting of a state space, a set of observables, and a dynamical law. We introduce constraint operators acting on the space of candidate theories, encoding symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a constraint-based interpretation of physical laws as consistency conditions. This framework provides a unified mathematical perspective in which classical mechanics, relativity, and quantum theory can be understood as different realizations within a common structure. This work presents a preliminary but structured conceptual and mathematical framework.