Universal Criticality and Finite-Size Scaling in Arithmetic Tensor Networks: Empirical Validation of the GUE Limit and the ν ≈ 2/3 Topological Phase

This upload contains the pre-print manuscript and supporting figures for the paper: "Universal Criticality and Finite-Size Scaling in Arithmetic Tensor Networks: Empirical Validation of the GUE Limit and the ν ≈ 2/3 Topological Phase" (PROMETEO-PRIME Part II). Abstract: Following the establishment of the coupled MERA-Fluctuation flow equations (PROMETEO-PRIME), this paper presents a rigorous mechanical-statistical validation of the infrared stable fixed point governing the non-trivial zeros of the Riemann zeta function. To refute potential finite-size artifacts and spectral overfitting, we perform a high-resolution Finite-Size Scaling (FSS) audit across 13 distinct computational scales. By analyzing the adjacent gap ratio r scaling towards the Gaussian Unitary Ensemble (GUE) expectation, we extract a highly stable critical exponent ν = 0.6702 ± 0.0069. The system demonstrates a flawless data collapse onto a universal scaling function with a relative error of merely 2.65%, converging definitively to a thermodynamic limit of χc(∞) = 28.4923 ± 0.057. Furthermore, a strict sensitivity analysis reveals a deep potential well for the critical exponent, ruling out artificial parameter tuning (RMSE ≈ 0.05378). The emergence of ν ≈ 2/3 strongly suggests that the entanglement-driven topological phase transition along the critical line belongs to a universality class analogous to 3D percolation or random graph cluster formation in the Mellin space. These results provide conclusive empirical evidence that the GUE limit is an intrinsic, scale-invariant property of the arithmetic bulk, independent of architectural truncation. Key Findings: Empirical FSS Audit: Execution of a 13-scale Finite-Size Scaling sweep to validate thermodynamic stability. Critical Exponent Extracted: ν = 0.6702 ± 0.0069, linking the Riemann zeros' distribution to 3D percolation and random graph topological phase transitions. Absence of Overfitting: Demonstrated via strict sensitivity analysis, data collapsing, and a residual RMSE of 0.05378. Thermodynamic Limit: Confirmed structural convergence at χc(∞) = 28.4923. Files included in this repository: Full manuscript (PDF) High-resolution empirical figures (FSS audit, Residuals, Data Collapsing, and Sensitivity Analysis)