RigbySpace: A Discrete, $\pi$-Free Blueprint for Fundamental Physics

We present a formal derivation of the RigbySpace (RS) framework: a deterministic, discrete, and $\pi$-free reformulation of classical and quantum field theories. Replacing the continuum with saturating AT/TA transformations and using the fundamental RS constants $\text{VEN} = 22$ and $\text{LUC} = 7$, we introduce a finite, recursive structure governed by rational ratios such as $22/7$ and $7/19$. We show that RS reproduces the anomalous perihelion precession of Mercury and propose a pathway toward solving the Yang--Mills mass gap problem using a recurrence-induced spectral gap. This work provides the mathematical skeleton and physical implications of RS, offering a fresh deterministic foundation for the universe's architecture.