Special Applied Supplement: Analytical Derivation of Non-Markovian Logarithmic Anomalies in Monojet LHC Spectra (150–350 GeV) from First Principles of von Neumann Algebras

We report the exact derivation of the non-perturbative logarithmic spectral template (Phi_KMS) from the modular automorphism group of the crossed product von Neumann algebra N = M_III_1 x_alpha R. Utilizing the framework of Noncommutative Geometry (NCG), we demonstrate that under a non-stationary external gauge perturbation violating the semi-classical Ward-Slavnov-Taylor identities, the open quantum geometry dynamics transition into a parametric resonance of the Nakajima-Zwanzig memory kernel K(tau). This forces a localized deformation of the Connes spectral action trace within the 150 GeV <= E_T^miss <= 350 GeV kinematic corridor of hard parton scattering. The resulting asymmetric fractal distribution is topologically protected by the Atiyah-Singer index theorem on the underlying type II_infinity factor. We demonstrate that the confirmation of this spectral distribution operationally establishes the retrocausal, non-local framework of the Loop Quantum Gravity (LQG) spin network inside a static four-dimensional Block Universe as the unique mathematically consistent ontology of physical reality. Explicit, parameter-free falsification metrics under the Pearson chi^2/ndf criteria are established for immediate verification via High-Luminosity LHC datasets.