This monograph delivers a rigorous, non-perturbative reconstruction of the space-timecontinuum natively within the internal language of the smooth, cohesive ∞-topos H = Sh∞ (ArithSite). We replace the classical continuous geometric background with an abstract motivic cochain complex C u2022 (M), modeling the complete information boundary network as a global adélic variety evaluated over the restricted product ring AQ = R × ∏︁p u2032 Qp. By upgrading general relativity to the dual tensor dynamics of Einstein—Cartan theory, the physical constants of nature (ℏ, c, G) and the standard Lorentz transformations emerge natively as the global constants of holomorphicity and absolute arithmetic tracking stabilizers required to balance metric curvature (Tµν) and spin-density torsion (Σ µνλ ) across scale horizons.We demonstrate that the Riemann Hypothesis (RH) is a mandatory global stability theorem protecting the space-time manifold from catastrophic geometric dissolution. Spacetimematerializes when information-packet density overloads the Maximum Distance Separable(MDS) Singleton bound of a rootless, norm = 4 Leech Lattice (Λ24) vacuum. To absorb this 5-bit information debt, the universe invokes the degree-4 Fermat curve, branching thepre-geometric bulk into a genus-5 multi-handled Riemann surface. The non-trivial Riemannzeta zeros are unmasked as the exceptional, lossless impedance sinks (χ u2032 = χ u2032u2032 ≡ 0) of anadélic waveguide, satisfying a universal periapsis turning point condition over the contractible Grothendieck Motive. At these precise coordinates, the tangential acceleration vanishes identically (aθ = 0) while the centripetal acceleration hits an absolute, max-plus tropical extremum (ω 2 = −2E = Max). Any spectral deviation off this axis triggers an instantaneous, infinite negative Ruppeiner metric divergence (g uu Rup → −∞), rupturing the Einstein tensor and causing the continuum to dissolve into chaotic bit-scrambling.