Abstract In the preceding papers of the G-MaTT Mathematical Foundations series, we constructed the algebraic (Paper I), group-theoretic (Paper II), and geometric (Paper III) foundations of emergent spacetime. In this fourth and final foundational paper, we derive the dynamical laws of physics. We apply the Connes-Chamseddine Spectral Action Principle to the \(G_2\) quasi-crystalline spectral triple \((\mathcal{A}, \mathcal{H}, D)\) constructed in Paper III. We demonstrate that the asymptotic expansion of the trace \(\text{Tr}\left(f\left(D/\Lambda_{\text{TUT}}\right)\right)\),where \(\Lambda_{\text{TUT}}\) is the Twist-Untwist Threshold cutoff, reproduces the full Standard Model Lagrangian coupled to Einstein-Cartan gravity. Specifically, we show how the Seeley-de Witt coefficients \(a_0, a_2, a_4\) generate the cosmological constant, Einstein-Hilbert term, and Yang-Mills/Higgs actions respectively. Crucially, because the spectrum of \(D\) possesses a natural spectral gap at \(\Lambda_{\text{TUT}}\), all loop corrections are finite without renormalization, as the heat kernel trace converges exponentially. We derive the running of coupling constants from the \(a_4\) coefficient and demonstrate that they unify at the scale \(\Lambda_{\text{TUT}}\) due to the underlying \(G_2\) symmetry. This work completes the constructive derivation of physical laws from pure geometry, establishing G-MaTT as a fully dynamical, zero-parameter theory.