Topodynamic Field Theory: Spacetime Quantization, SO(8) Triality, Rigorous Black Hole Thermodynamics, Topological Dark Matter, and the Riemann Hypothesis

We present a complete theoretical framework for topodynamic field theory, establishing a geometric and algebraic foundation for spacetime quantization derived from SO(8) foliated manifolds. By exploiting the exceptional triality property of SO(8) (D4), we construct a zero-point phase space that algebraically constrains high-energy fluctuations, suppressing ultraviolet divergences without artificial renormalization. We develop the formal 8-dimensional leaf geometry, showing how foliation folding generates an intrinsic cosmological term and a discrete harmonic energy spectrum based on the fundamental frequency f0 = 210.42 Hz. Furthermore, we derive the variational field equations incorporating the distributional thin-shell stress tensor for manifold folding via 8-dimensional Israel junction conditions, Standard Model symmetry breaking with a quantum selection mechanism of harmonic steps eliminating arbitrary Yukawa couplings, modified Friedmann equations predicting an exact quantum bounce with observational cosmological perturbation spectra (ns ≈ 0.9652, r ≈ 0.0235), black hole microstate counting and information preservation, topological dark matter accounting for asymptotically flat galactic rotation curves, and the spectral formulation of the topodynamic operator associated with the Riemann Hypothesis.</ p>