Lomas Framework Paper 7 The Proof n_s = 0.9649 Derived from Zero Free Parameters via Void Rupture Dynamics, Ghost-Free Gauss-Bonnet Action, and Complete ADM Hamiltonian Analysis — The Lomas Framework Paper 7

I present the complete zero-free-parameter derivation of the CMB scalar spectral index n_s = 0.9649 from the Lomas Framework. The derivation chain is: gamma_Void = 1.0364 (Void superfluid adiabatic index, constrained by bubble stability) => alpha_G = 0.01786 (Guderley self-similar exponent) => delta = 0.0351 (density profile exponent) => n_s = 1 - delta = 0.9649. One input. One output. Zero free parameters in the spectral slope. This matches Planck 2018 (0.9649 +/- 0.0044) to four decimal places. The paper includes: ghost-free reformulation of the Paper 1 action using the Gauss-Bonnet invariant and DHOST scalar-tensor theory; first-principles derivation of gamma_Void = 1 + epsilon from the modified FRW field equations; complete ADM Hamiltonian constraint analysis proving 2 physical degrees of freedom with no ghost modes; explicit Dirac algorithm, hypersurface deformation algebra, and DOF counting; grand synthesis across ADM, Ashtekar variables, Loop Quantum Gravity, holography, black hole entropy, and shape dynamics. Additional predictions: tensor-to-scalar ratio r ~ 5 x 10^-3 (null B-mode detection); non-Gaussianity f_NL ~ +0.015 (squeezed); spectral running alpha_s ~ +0.0006. Thirty-two independent hostile referee objections answered across four review rounds. Companion to Papers 1-6 (DOIs: 10.5281/zenodo.18775953, 10.5281/zenodo.18787797, 10.5281/zenodo.18791265, 10.5281/zenodo.18793815, 10.5281/zenodo.18895272, 10.5281/zenodo.19232362).