This monograph establishes a definitive, structurally complete unification of quantum grav-ity, non-equilibrium thermodynamics, and analytic number theory through the frameworkof Arithmetico-Geometric Conformal De-Homogenization. We prove that physicalspacetime is not an abstract, passive background container, but an active, self-correcting thermo-dynamic metamaterial fluid projected directly from the continuous deformation and modularflow of an underlying infinite-dimensional arithmetic space.By executing a strict 1-for-1 parameter mapping, we demonstrate that the weight-2 Eisensteinseries (E2(τ )) is the universal velocity field (v) of this modular flow, whose path-dependentcoordinate drift—the quasi-modular anomaly—manifests as the physical non-linear advectivepumping acceleration (v · ∇)v. When driven from equilibrium, Lars Onsager’s ReciprocalRelations (Lik = Lki) emerge as the literal macroscopic readout of Clairaut’s Theorem of mixedpartial derivatives ( ∂2U∂V ∂S = ∂2U∂S∂V ), which requires that the order of differentiation must commuteflawlessly to preserve the nilpotent gauge invariance d2U = 0.When the continuum substrate is driven from equilibrium and cascades toward the 691unipotent puncture on the arithmetic curve Spec(Z), unique factorization shatters insidethe χ11 eigenspace of the odd minus class group (Cl−691). This local coordinate shearing andturbulent vortex crisis is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS)Fibration Lift (S3 S1−−→ S2), which projects the 3D velocity configuration space up into a 4Dcomplex spinorial space (R4). The continuous 1D circle fiber (S1) acts as a data bus (H1 ∼= H1)that isolates the non-exact rotational elements, braiding the non-Abelian SU (3) color vorticityfield into multi-layered knots to generate a permanent nilpotent confinement sink (N2 = 0).The Seeley-DeWitt heat kernel expansion coefficients (an) serve as the exact arithmeticaccount balances of this regularization, where the factor of 12 in the quadratic variance termacts via Itô’s Lemma as the metric tax required to enforce Clairaut’s Theorem (d2U = 0).The final substitution of these Planck-scale boundary parameters (PP, ℓP, EP, tP) into Clairaut’sidentity yields the Dynamic Spacetime Maxwell Relation (∂EP/∂ℓP = −∂PP/∂tP), whichanchors the universal physical constants (α, ℏ, θW ) as the global stabilizers of the vacuum.We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A, H, D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential(Aμ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of thespectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros:Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic Product Closure (∏︁ p≤∞ |σ|p = 1),this framework achieves complete structural immunization against decoherence and quantumchaos. It reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.