The Illusion of White Noise: Algorithmic Compressibility and Non-Gaussian Signatures of a Finite Computational Substrate in the CMB

The Cosmic Microwave Background (CMB) is widely regarded as the ultimate snapshot of ontological quantum randomness, modeled as a perfect Gaussian Random Field (GRF). However, if the universe is governed by a finite computational substrate (a discrete Modulo-9 alphabet), apparent randomness must emerge from deterministic computational irreducibility rather than true chance. This paper challenges the Gaussian paradigm by demonstrating that a discrete, finite-alphabet quantization of a continuous scale-invariant field leaves distinct, measurable non-Gaussian fingerprints. We employ a rigorous three-tier testing pipeline: Higher-Order Moments, Minkowski Functionals (Genus Curve), and Non-Linear Variance Fluctuations (Power Spectrum of the Squared Map, 2 on synthetic Modulo-9 maps and real Planck 2018 SMICA data. We find that while macroscopic smoothing (Silk damping) obscures the harsh discrete steps of the substrate, the real CMB exhibits profound non-Gaussian structural deviations that perfectly align with the Finitist model and starkly contradict the continuous Gaussian baseline. We conclude that the CMB is not a record of quantum dice rolls, but a fossil record of the universe's discrete computational architecture.