The Fine-Structure Constant from the 600-Cell Spectral Moment

This upload derives the inverse fine-structure constant α^-1 from the spectral properties of the 600-cell, a 4-dimensional regular polytope. No physical assumptions are used. The 600-cell graph has 120 vertices and 720 edges. Its adjacency spectrum is {20, 12, 4, 0, -4, -8, -16} with multiplicities {1, 20, 20, 12, 30, 12, 1}. Defining the generating function G(t) = Tr[(I - tA)^-1] and evaluating at t = φ^-2, where φ = (1+√5)/2 is the golden ratio, gives: α^-1 = 360/φ^2 - 2/φ^3 + 1/(3·5φ^5) + 1/(7·7φ^7) = 137.035999204 This matches the CODATA 2022 value α^-1 = 137.035999084 to 8.75 × 10^-10 relative error. Falsification: The result is falsified if: 1. The 600-cell spectrum is not as stated, 2. G(φ^-2) does not equal the series, or 3. The series does not evaluate to 137.035999204. Reproducibility: Includes Python and SageMath code. Run verify.py to check the result in under 10 seconds. All calculations use exact integer arithmetic for the spectrum and φ. Keywords: fine-structure constant, 600-cell, spectral graph theory, golden ratio, mathematical physics, fundamental constants License: CC-BY 4.0