Geometric Origin of the Fine Structure Constant: 1/α = 4π³ + π² + π

We demonstrate that five fundamental constants of the Standard Model are expressible as rational functions of π with small integer coefficients, each matching experiment to within one standard deviation with zero free parameters. The fine structure constant satisfies the equilibrium condition 1/α + α/D = G_π, where G_π = 4π³ + π² + π and D = 24 − 1/(8π), yielding α⁻¹ = 137.035999215, deviating by 0.8σ from the Rb-2020 measurement (Morel et al., Nature 588, 61, 2020). We provide a geometric derivation in which the three terms correspond to bulk (3D), surface (2D), and core (1D) electromagnetic mode contributions, with mode density 3π² arising from the volume of the rotation symmetry group SO(3)/Z₂. The framework extends to four additional constants:- Weak mixing angle: sin²θ_W = π/(4π+1) = 0.2316 (0.3σ)- Strong coupling: α_s(M_Z) = 1/(3π−1) = 0.1187 (0.8σ)- Proton-electron mass ratio: (π⁷−9π⁶+75π⁵−27π⁴)/8 = 1836.1527 (1.0σ)- Tau-electron mass ratio: 12π⁵−2π⁴+π³−6π²+9π = 3477.48 (0.0σ) The balance equation is presented as a geometric postulate (analogous to Bohr's quantization condition) rather than a derivation. Explicit falsification criteria are provided, including a near-term Rb-vs-Cs experimental fork: the formula agrees with the Rb-2020 value at 0.8σ but disagrees with the Cs-2018 value at ~6σ. This paper supersedes the preliminary version (doi:10.5281/zenodo.18476593). Supplementary file: supporting_computations.py reproduces all numerical claims using only the Python standard library. Run with: python3 supporting_computations.py Contact: john@northernlights.co.nz