Adelic Symmetry Breaking and Mori–Zwanzig Kernels: Complementary article to Adelic Self

This paper presents a unified resolution to four long-standing structural problems(F1–F4) within the G∞-RCD(QAP) framework of quantum gravity. By integratingrecent advances in p-adic number theory, Mori–Zwanzig (MZ) memory kernelformalism, and supersymmetric adelic field theory, we demonstrate that a positivecosmological constant is mathematically necessary for the path integralconvergence. We identify the Standard Model Weyl anomaly coefficient |ζ' (0)|= 11/180 as the precise measure of adelic symmetry breaking, which determinesthe vacuum energy through an electroweak hierarchy truncation at depth N ≈39.34. The resulting "Expansion-Convergence-Resolution Identity" proves theequivalence of Λ > 0, the Euclidean GHP contour rotation, and the resolution ofthe isospectral discrimination problem (F2). We derive the exact Mori–Zwanzigmemory kernel for the superspace transition operator, yielding characteristiceigenvalues λ₁ ≈ +0.449 (growing tensor mode) and λ₂ ≈ -0.816 (decaying scalarmode). The decaying mode improves the Point Spread Function (PSF) resolutionfrom 10⁻⁸ to ~1.5 × 10⁻¹⁴, enabling the discrimination of isospectral non-isometricmanifolds by six orders of magnitude. Furthermore, we establish a four-vertexconsistency triangle where the spectral gap γ = 11/30 is independently validatedby the Bruhat-Tits tree structure, Vladimirov fractional calculus, InformationGeometry, and the Standard Model Weyl anomaly. This framework thus bridgesthe gap between p-adic number theory and observable quantum cosmology.