Adaptive Constraint Cascade (ACC): Part 0 – Foundations (A Working Definition for Continuous Transitions Between Physical Theories)

We propose a tentative working definition of an Adaptive Constraint Cascade (ACC) – a framework for describing continuous transitions between distinct physical theories via a deformation of their underlying effective structural relations. An ACC is defined as a tuple (P, T, {C_p}, Φ) satisfying a set of heuristic axioms. The parameter space P is a connected topological space (e.g., an interval in R or a product of intervals). For each p in P, T(p) is a physical theory, and C_p denotes its associated effective structural relations (e.g., commutation relations, master equations, or constraint algebras). The family {C_p} is required to vary continuously with p in an appropriate sense. We show that the three case studies – ACC_1 (quantum–classical transition), ACC_2 (Newton → SR → GR), and ACC_3 (NRQM → QFT) – are instances of this definition. This foundational paper provides a coherent structural language for future developments, including categorical formulations and testable predictions, while remaining deliberately open to refinement.