The Topological Origin of Mass and Charge: Deriving Fermionic Properties from a Discrete Möbius Substrate

Standard physics treats the Fine Structure Constant (), rest mass, and the Pauli Exclusion Principle as fundamental, irreducible properties of the universe. This paper proposes a radical alternative: these properties are emergent artifacts of a discrete, finite computational substrate governed by Modulo-9 arithmetic. We demonstrate that the continuous constant is an illusion of macroscopic averaging, replaced at the Planck scale by a topological 4 symmetry inherent to a Möbius lattice. Through three distinct computational simulations, we derive: (1) Rest Mass as "topological friction" (computational inertia) arising from the 4 phase twist; (2) The Pauli Exclusion Principle as arithmetic saturation preventing identical topological defects from occupying the same lattice space; and (3) The Fine Structure Constant (≈ 1/137) as the energetic "tax" a defect must pay to shed radiation and maintain coherence during phase transitions. This framework unifies particle physics with cosmological observations, specifically the low-power deficit and algorithmic compressibility of the Cosmic Microwave Background (CMB).