S²-11DM²ET-X Model: Mathematical Proof of Unification

This publication provides the complete, self-contained mathematical proof of the S²-11DM²ET-X unification model's predictive power. The entire structure is derived parameter-free from the axiom of exactly three fermion generations. This axiom forces the non-perturbative M-theory superpotential W_np = e³, flux budget N_flux = 4880, and the Hampton Qutrit Collatz Convergence (HQCC) theorem, the ternary qutrit map that collapses in exactly 539 steps in the 11D bulk and projects to a 55-step classical orbit on the (3+1)D +U brane. From this single dynamical system we derive all Standard Model parameters, including fermion masses (explicit eigenvalues of generational matrices), CKM/PMNS mixing (from diagonalizing unitaries), and cosmology. All quantities emerge without free parameters from the three-generation axiom alone.