Parameter-Free Derivation of the Fine-Structure Constant α = 1/137 from the S²-11DM²ET-X Higher-Dimensional Framework and the Hampton Qutrit Collatz Convergence (HQCC) Theorem: Topological Leakage and the Unified Origin of Electromagnetism and Magnetism

We present a mathematically rigorous, parameter-free derivation of the fine-structure constant α ≈ 1/137 within the S²-11DM²ET-X model. Starting from the three-generation axiom of fermions and the HQCC theorem—which establishes exact convergence of all physically allowed qutrit states in 539 ± 1 steps, fixing the immutable cosmic flux period T = 539.9 s—the electromagnetic coupling emerges as the irreducible leakage probability λ across the D2-brane debit-repayment cycle. Combinatorial enumeration in the resonant number theory and RTTC spectral sequence yields an effective number of coherent repayment channels N_eff = 137, so that α = 1/N_eff exactly at tree level (with higher-order corrections reproducing the observed 1/137.035999…). The same leakage mechanism, when interpreted through the S² compactification of the 11D manifold (Euler characteristic χ(S²) = 2 and π₂(S²) = ℤ), naturally produces the circulatory/vorticial component identified as magnetism in 4D. Magnetic fields arise as the angular projection of the brane flux cycle, unifying electric and magnetic phenomena under a single topological leakage. The framework is internally consistent, closes via Noether-derived friction, and ties to biological scales through 40 GHz tubulin synchronization. This construction offers a unified geometric origin for electromagnetism without free parameters.