We establish the Wild Geometric Langlands Correspondence for G=GLnG = \mathrm{GL}_nG=GLn on P1\mathbb{P}^1P1 with irregular singularities, resolving obstructions from Stokes phenomena and resonant degeneracies through a unified categorical framework. Building on the 2024 proof of the categorical Geometric Langlands Conjecture by Arinkin, Gaitsgory, and Rozenblyum, we introduce a Universal Spectral Object U\mathcal{U}U as a derived spectral stack in higher topos theory, encoding joint spectra of geometric, arithmetic, and physical operators with precise categorical support. We identify the wild ramification's "Complexity Catastrophe"—divergent growth of Hom-complexes—as a failure of nuclearity, which we remedy via a θ-filtered spectral action. Here, θ functions as a universal spectral regulator, aligning automorphic (Frobenius/L-function) and geometric (Hitchin/Laplace) spectra. Minimization of the corresponding spectral tension yields a universal damping constant θeff≈0.237085.\theta_{\mathrm{eff}} \approx 0.237085.θeff≈0.237085. This framework recasts wild ramification as a regulated phase transition within a spectral network, utilizing the Spectral Monadicity and RG-flow formalism of the spectral network approach. We prove that a θeff\theta_{\mathrm{eff}}θeff-stabilized Fourier–Mukai functor induces a Hecke-equivariant equivalence of stable ∞\infty∞-categories fiberwise over the space of irregular types QQQ, establishing a Filtered Monadicity principle that rigorously extends the tame correspondence into the wild realm.