A Discrete, Recursive, and $\pi$-Free Blueprint of the Universe

We present a formal and exact reformulation of physical law based on the RigbySpace (RS) framework: a discrete, saturating, and recursive alternative to the continuum of general relativity and the wavefunctions of quantum theory. The RS model excludes transcendental constants such as $\pi$, $e$, and $\phi$, replacing them with rational, finite operations grounded in two fundamental constants—VEN and LUC—whose ratio generates angular structure, field strength, and spectral growth. By reconstructing spacetime curvature from recursive difference equations and replacing the exponential function with saturating algebraic trigonometry, we reveal a deterministic and unified structure of the cosmos. The presence of a quantized spectral gap arises naturally from imbalance in recursive sequences. We derive the RS field equations, construct the discrete Ricci tensor, and present explicit examples of physical phenomena emergent from this framework.