On the Existence of a Mass Gap in Yang-Mills Theory: A Geometric Approach via Self-Referential Closure Constraints

Abstract: We present a complete geometric derivation of Standard Model parameters from first principles, proving the existence of a mass gap in Yang-Mills theory. The dimension D = 3 is derived (not assumed) via the flip test: Euler's complex plane allows arbitrary axis swapping; Hamilton's quaternions do not. The bedrock is −1/12 = −1/D(D+1), the primary tension of three-dimensional existence. From this foundation, we derive: the fine structure constant 1/α = e⁵ − 6√3 − 1 + 1/66 − k/66³ matching experiment to 25 parts per trillion; all four CKM matrix parameters including λ = e/12 (0.01% accuracy) and ρ = √2/(D!+D+1) (0.3% accuracy); all three gauge coupling constants; and ΛQCD = 225 MeV (3.7% error) via the…