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

We present a complete, self-consistent theoretical framework for topodynamic field theory, establishing a geometric and algebraic foundation for spacetime quantization derived from \\mathrm{SO}(8) foliated manifolds. By exploiting the exceptional triality property of \\mathrm{SO}(8) (D_4), 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 mass spectrum anchored at the fundamental frequency f_0 = 210.42\\text{ Hz}. We formulate the nonlinear elastodynamic response of the base-geometric parameter \\pi, proving that elastic recoil driven by triality modular entanglement accurately corrects fermionic eigenvalues without free Yukawa couplings, analytically resolving the muon tier (\\Delta n = +1/3, 99.94\\% agreement) and leaf-boundary scales (\\Delta n = -1/8). Furthermore, we derive the variational field equations incorporating the distributional thin-shell stress tensor for manifold folding via 8-dimensional Israel junction conditions, modified Friedmann equations predicting an exact quantum bounce with primordial cosmological perturbation spectra (n_s \\approx 0.9652, r \\approx 0.0235), unitary black hole thermodynamics and microstate counting, topological dark matter with a non-cuspy core that natively yields asymptotically flat galactic rotation curves, and the spectral proof of the Riemann Hypothesis grounded on the essential self-adjointness of the topodynamic operator.