The Universal SDRIS Zeta-Regularization Theorem: Isoclinic ϕ-Rotations, p-adic Stability, Geometric Duality, and Hierarchical Structure in Coxeter and Kac-Moody Lattices

We establish a universal closed-form expression for the optimal spectral zeta-target \(c(N,W)\) governing the regularized sum of Laplacian eigenvalues of any projected Coxeter root lattice after isoclinic \(φ\)-rotation:\[c(N,W) = -{σ̃^2(W)}{4} + ( {σ̃^2(W)}{4} - 1/12 ) N-1/2,\]where \(σ̃^2(W)\) is the modified variance determined by the Coxeter exponents of the (finite, affine or hyperbolic) group \(W\). This formula interpolates exactly between the discrete Casimir point \(c(N→ 0,W) = -1/12\) and the continuous Wigner bulk \(c(N→∞,W) = -σ̃^2(W)/4\), satisfies a universal quadratic Stieltjes equation, and is strictly monotonic and convex. A geometric duality relates the Casimir regime to the unit-square diagonal \(√2\) and the Wigner bulk to the unit-circle quadrature \(π\). The target remains stable under arbitrary prime-adic completions, converging hierarchically to the eighth shell \(S_8\) of the \(p\)-adic ultrametric topology. The result holds uniformly for all irreducible Coxeter groups and their Kac--Moody extensions. The dual formulation obtained by the substitution \(M=N⁻¹\),\[c^*(M,W) = -1/12 + ( {σ̃^2(W)}{4} - 1/12 ) M1/2,\]realizes an alternating transformation between the discrete Casimir vacuum and the continuous macroscopic field, thereby unifying spectral graph theory, number theory, and exceptional algebraic geometry. Data Availability: The complete Python source code used for the numerical validation of the scaling collapse, moment recursion, p-adic trajectories, and 8-shell hierarchy is permanently archived on Zenodo and can be accessed via DOI: 10.5281/zenodo.1958148.