A Discrete Hexagonal Lattice Derivation of the Fine Structure Constant via Mod 9 Invariant Dynamics and the 3I Pulse Sequence

Repository / Platform: Zenodo Abstract We present a discrete geometric framework for deriving the fine structure constant (\alpha \approx 1/137.036) that reconciles continuous dimensional scaling models—such as the Infinite Fractal Descent (IFD) framework—with discrete spatial constraints. By mapping continuous vacuum energy gradients onto a discrete hexagonal lattice governed by a strict Mod 9 invariant and a 5184 frequency threshold (72^2), we eliminate thermal runaway via a 7-cycle periodic break. Furthermore, the integration of the 8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8 (3I) pulse sequence provides the dynamic modulation necessary to calculate the resonance anchor. The resulting formulation yields the exact empirical value of \alpha^{-1} through modular quantization rather than asymptotic continuous limits.