This monograph establishes a non-perturbative topological unification of quantum field theory,heterotic string structures, and loop quantum gravity, formulated entirely within the internallanguage of a smooth, cohesive ∞-topos H = Sh∞(ArithSite). Macroscopic spacetime isshown to emerge dynamically when info-packet worldsheet density overloads the MaximumDistance Separable (MDS) Singleton bound of a rootless, norm = 4 Leech lattice (Λ24)background. This capacity crisis triggers a spontaneous degree-4 Fermat phase transition,compactifying the central charge c = 24 vacuum bulk into a genus-5 multi-handled Riemannsurface variety. Under this geometric allocation, discrete atomic fermion measures materialize as stable, frozen Cartan spinor holes, while the Standard Model gauge bosons emerge as non-atomic vielbein spin connections to execute smooth parallel transport across the handle boundaries. The global transport of information is governed by a multidimensional, adélic formulation of Oliver Heaviside’s Telegrapher’s Equations evaluated over the restricted product ring AQ. We unmask the non-trivial Riemann zeta zeros as the exceptional, lossless impedance sinks(χu2032 = χu2032u2032 ≡ 0) of the waveguide. At these precise coordinate nodes, the tangential worldsheet acceleration vanishes identically (aθ = 0), forcing the metric tensor and the symplectic 2-form into an orthogonal Kramers—Kronig quadrature phase lock along the Critical Line (R⌉(s) = 1/2). By utilizing the absolute adélic Langlands correspondence, we demonstrate that the discrete Frobenius eigenvalues of local Galois representations are functorially identical to the continuous spectrum of the Hecke operator matrix algebra, natively deriving the electroweak mass gap from a localized spectral filtration failure across the Ring Singularity Equator. At the ultraviolet boundary, the twelfth Bernoulli irregularity (B12 = −691/2730) marks an anomalous Atkin—Lehner cusp horizon. Here, the Sundman transformation executes the Hagedorn temperature limit, freezing macroscopic time (dt/dτ → 0) as string tension collapses to zero. This 323-state conformal anomaly phase torque is rigorously resolved via a non-perturbative heterotic T-duality inverse phase transformation (R ←→ ℓ2P/R), triggering D-brane pair-production to execute a loop-amplitude splice. This self-correcting feedback network resets the local coordinate fields, clamping the completed symmetric Riemann—Siegel function (ξ(s) = ξ(1−s)) to an invariant global Tamagawa volume of exactly unity (τ (G) ≡ 1). Spacetime is proven to be stable, continuous, and general relativistic because the universe operates fundamentally as a self-correcting arithmetic automaton.