Recursive Geometric Closure as a Universal Fixed-Point Principle

This paper develops a purely mathematical framework built on the idea of recursive geometric closure acting on scale-free, projective configuration spaces. The core result is that a wide class of nonlinear closure operators admits a unique, globally attractive fixed point, independent of arbitrary choices such as norms, kernels, or response functions. The construction is intentionally adimensional and non-dynamical: configurations are defined only up to rescaling, and recursion enforces internal geometric consistency rather than evolution in time. Under mild assumptions of continuity and contractivity, closure selects a stable configuration that all admissible geometries converge to. A central consequence of this process is the emergence of universal geometric invariants. These invariants are not imposed by hand; they arise from the stability of the fixed point under iteration and coarse-graining. Because they are projectively defined, they are insensitive to scale, resolution, and representation. Physical interpretation is deliberately postponed: no spacetime, dynamics, or constants are assumed. Instead, the framework isolates a structural mechanism by which constants or effective laws, if they appear at all, must correspond to fixed-point invariants of a recursive geometry, rather than free parameters. The result is a clean separation between geometric consistency and phenomenology, providing a rigorous foundation for later emergent interpretations.