QUANTUM GEOMETRY REGULARIZATION AND THE EMERGENCE OF MACROSCOPIC TIME. Part IV: Distributed Collider Phenomenology, Pre-Geometric UV-IR Mixing, and Operator Dispersive Constraints on LHC Open Data within a 4D Block Universe

Abstract

This paper extends the foundational theoretical framework formulated in Parts I, II, and III of this research multi-volume, presenting a non-perturbative, data-driven phenomenological protocol for isolating the empirical signatures of Loop Quantum Gravity (LQG) area gaps and non-commutative space-time foam within high-energy collider physics without invoking multi-dimensional bulk-space extensions. Operating strictly within a four-dimensional pre-geometric Block Universe, we demonstrate that the integration of the regularized Gauss–Nicolini gravitational potential and the Relational KMS Interpretation of quantum mechanics systematically induces localized, non-linear UV-IR mixing at TeV scales (where the center-of-mass energy reaches 13-14 TeV).To overcome the standard Planckian power-suppression bounds in four dimensions, the effective open-system coupling is regularized via a fractal renormalization group flow over the Connes spectral action, where the information leakage is scaled by the total number of active quantum modes (approximately 10^120) of the holistic block continuum. The transition from the global, timeless vector state to localized open-system dynamics is modeled via state restriction onto the canonical crossed product algebra (M_III_1 crossed with R), evaluating the effective density matrix over a unital operator subalgebra via a finite-trace projector corresponding to the observer's macroscopic thermodynamic horizon.The resulting Markovian dissipation is computed within the exact, non-linear eigenbasis of the Generalized Uncertainty Principle (GUP) Hamiltonian, yielding an explicit calculation of the anomalous transverse momentum leakage into the static 4D block. We map these analytical predictions onto existing experimental anomalies, specifically identifying soft kinematic excesses in the monojet channels of the LHC. We present a parallelized computational template designed to interface directly with the petabyte-scale archives of CERN Open Data (Run 2 and Run 3) in the monojet channel, establishing strict Popperian criteria to isolate these quantum-geometric anomalies from standard Standard Model backgrounds.