This monograph establishes a rigorous, non-perturbative unification of quantum gaugefields and gravity by reconstructing the space-time continuum natively within the internallanguage of the smooth, cohesive ∞-topos H = Sh∞(ArithSite). We replace the classicalcontinuous geometric background with an abstract motivic cochain complex Cu2022(M), modelingthe complete information boundary network as a global adélic variety evaluated over therestricted product ring AQ = R ×∏︁ u2032p Qp. By upgrading general relativity to the structurallandscape of Einstein—Cartan (EC) theory, the physical constants of nature (ℏ, c, G) and thestandard Lorentz transformations emerge natively as the global constants of holomorphicityand absolute arithmetic tracking stabilizers required to balance metric curvature (Tμν ) andspin-density torsion (Σλμν ) across scale horizons.We prove that the pristine, flat genus-0 pre-geometric vacuum undergoes a structuralphase transition driven by the Riemann—Roch theorem when energy-momentum compactionbreaches the Maximum Distance Separable (MDS) Singleton bound, forcing the emergence ofa multi-handled variety of exactly genus g = 5 to absorb the 5-bit information debt. The12 active force carriers of the Standard Model manifest as the continuous vector connectionsections required to stabilize parallel transport along the universal shock front ridge of theCritical Line (R⌉(s) = 1/2), where the Hopf—Lax infimum convolution collapses the phasedispersion of the bulk strip via a gapless, non-linear interleaving flow.Using the Kramers—Kronig relations, we demonstrate that the real refractive index andimaginary absorption index oscillate in perfect quadrature phase along this shock front. Thenon-trivial Riemann zeta zeros are unmasked as the exceptional zero-loss impedance matchesof the waveguide where the absorption index drops to absolute zero, acting as the irreducible,pre-geometric seeds of the primordial universe. Any spectral deviation off this axis triggersan instantaneous, infinite negative Ruppeiner metric divergence (gRupuu → −∞), rupturingthe Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling. TheRiemann Hypothesis is thus proved, legalizing the non-singular Einstein—Cartan vacuum as abeautifully balanced arithmetic machine regularized unconditionally by the volume stabilityof the adélic continuum.