FKX Constraint-Driven Discrete Formal Systems

FKX introduces a family of constraint-driven discrete formal systems for determining whether a system admits any genuine structural degrees of freedom.The central claim is that a system’s effective degrees of freedom are determined by the structure of its legal solution sets (“worlds”), rather than by the dimensionality of state representations, the size of the state space, or the apparent complexity of local dynamics. Under the joint conditions of hard constraints, closure under transitions, absence of external parameters, and reachability-based world semantics, FKX proves that even systems exhibiting non-trivial evolution are zero-dimensional in the sense that no independent adjustable parameters are required to index their worlds. The framework further provides three minimal counterexample templates, showing that introducing a single external parameter, allowing a single non-closed transition, or softening hard constraints into tunable weights is sufficient to immediately break zero-dimensional rigidity. FKX is not proposed as a modeling technique or a dynamical theory, but as a prior structural decision framework, intended to determine—before computation, search, or learning—whether a system structurally admits any expandable degrees of freedom at all.