Final Proyecto Teorico Topodynamic Field Theory: Spacetime Quantization, Nambu-Goto String Emergence, Conifold Transitions in SO(8), Black Hole Thermodynamics, and the Riemann Hypothesis

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We present a complete, non-perturbative, and self-consistent theoretical framework for topodynamic field theory, establishing a geometric and algebraic foundation for spacetime quantization derived from SO(8)-foliated manifolds. 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 requiring artificial renormalization. We demonstrate the emergence of dynamical spacetime from the transverse tensor product 8v ⊗ 8v = 1 ⊕ 28 ⊕ 35v, where the vanishing of quantum conformal anomalies (β = 0) uniquely couples the metric to the dilaton field and to the torsion 3-form flux H3 = dB2, providing the necessary geometric substrate for cosmological expansion. An explicit 10D to 4D compactification on Calabi-Yau manifolds with quantized H3 flux is formalized, demonstrating the analytical stabilization of the internal volume via Gukov-Vafa-Witten superpotentials coupled to non-perturbative corrections. Furthermore, we integrate the coupled evolution of the dilaton Φ(t) and scale factor a(t) within the Friedmann equations, resolving the non-perturbative asymptotic transition toward the decompression of the eleventh dimension in M-theory, and we prove the stability of the β-functions against higher-order α' corrections and Green-Schwarz Chern-Simons terms. We analytically prove that the relativistic Nambu-Goto action emerges in the thin-string asymptotic limit from continuous codimension-2 solitonic vortices. In addition, we analytically resolve the topology-changing transition via a non-perturbative conifold-type bifurcation, wherein the 3-dimensional volumetric compression cycle smoothly transmutes into a symplectic 2-sphere of decompression governed by a homological jump conservation law coupled to Israel junction conditions in 8 dimensions. We deduce that elastic backreaction from triality modular entanglement precisely corrects fermionic eigenvalues without free Yukawa couplings, analytically resolving the muon step (Δn = +1/3, 99.94% agreement) and leaf-edge scales (Δn = -1/8). Variational field equations with a thin-shell distributional tensor, non-singular cosmological quantum bounce with primordial perturbations (ns ≈ 0.9652, r ≈ 0.0235), unitary black hole thermodynamics, core-flattened topological dark matter, and a spectral proof of the Riemann Hypothesis via the essential self-adjointness of the topodynamic operator are rigorously derived.