Geometric Derivation of the Fine-Structure Constant and Proton-Electron Mass Ratio in a VE55 Lattice Framework

This paper presents a revised deterministic lattice-topological framework in which the distinguished count Nₜₒₚₒ = 137 is decomposed into explicit integer-lattice contributions tied to a parity-disjoint VE55-BCC44 construction. The visible sector (VE55) is the even-parity subset of the scale-2 cuboctahedral hull with 55 vertices, while exactly 38 odd-parity vertices from the BCC44 lattice lie inside the same hull. Including the companion vacuum sector and 6 axial anchors, we prove the exact topological count Nₜₒₚₒ = 55 + 38 + 6 + 38 = 137. From this exact count and two geometry-derived areas (Avac = 16√3 and Aₘₐₜ = 48), we define a self-consistent fixed-point equation for the electromagnetic coupling. Its unique stable positive solution yields the fine-structure constant αgeo⁻¹ = 137.0359991744, which is numerically highly consistent with the CODATA reference value 137.035999177(21). Furthermore, a companion mass-ratio formula within the same framework produces the proton-electron mass ratio μgeo = 1836.1524966755, leading deterministically to a proton mass energy equivalent of mp,geo = 938.271999108 MeV. Methodology and Reproducibility To maximize scientific transparency and reproducibility while protecting proprietary implementations, the source code is withheld in this paper. Instead, all geometric definitions, the parity disjointness theorem, the fixed-point equation, and a minimal algorithmic pseudocode are stated explicitly, allowing for independent reimplementation by any researcher. Claim Boundary The paper maintains a strict claim hierarchy. The topological count 137 and the fine-structure constant are treated as deterministic mathematical outputs of the explicit VE55-BCC44 geometric construction (Layer A/B). Conversely, the additive electromagnetic correction in the mass-ratio formula is explicitly classified as a phenomenological extension (Layer C) at the present stage, establishing a clear boundary between mathematical necessity and physical hypothesis.