Emergent Causal Structure in 3+1D: Numerical Validation of the No-Go Theorem and Local Superluminality in TAGC-LQG-RG Theory

We present a numerical validation framework for the TAGC-LQG-RG Unified Theory, specifically focusing on the stability of the Emergent Causal Structure (Theorem 3.6) and the No-Go Theorem for Extra Dimensions (Theorem 3.4). The theoretical framework postulates that the speed of information transfer is dependent on the local informational density ($\rho$), allowing for local superluminal fluctuations ($v > c$) in low-density vacuum regions ("voids") while strictly preserving global causality through a hierarchical cone structure. To test this hypothesis, we developed a stochastic Monte Carlo simulation ("Toy Model") operating on a 3+1D toroidal topology with a heterogeneous scalar density field. Key Results: Local Superluminality: The simulation confirms the existence of local superluminal events (constituting 6.74% of trajectory steps) driven by quantum fluctuations in the low-density regime. Global Causal Preservation: Despite local violations, the global fraction of Closed Timelike Curves (CTCs) remained at 0.0000 ($N=1000$ trajectories). This indicates that the density-dependent velocity hierarchy acts as an effective "Asymptotic Censorship" mechanism. Robustness: A stress test forcing an instability regime (80% fluctuation probability) successfully resulted in causal collapse, validating the model's sensitivity and the physical stability of the TAGC parameters. These numerical findings support the conclusion that a 3+1D geometry with variable informational density is sufficient to resolve causal paradoxes, rendering 5D extensions superfluous. The code and data are provided for reproducibility. Keywords: TAGC-LQG-RG, Emergent Gravity, Causal Structure, Superluminality, No-Go Theorem, Monte Carlo Simulation, Quantum Gravity.