Xu-Based Spectral Diagnostics for 2D MHD: Benchmarks, High-Frequency Stress Tests, and a Publication-Grade Pipeline

This software and technical documentation present the Xu-AUDITOR protocol: a high-fidelity spectral auditing engine for 2D Magnetohydrodynamics. By implementing Xu-style modal convolutions, the tool achieves an algebraic precision of $10^{-14}$, allowing for the detection of spectral blocking and regularity breaks (notably at $t=0.266$) that are often invisible to standard pseudo-spectral solvers. Includes the complete Python pipeline, benchmarking suites, and publication-grade rendering tools. Key features: 2D incompressible MHD, spectral blocking detection, regularity monitoring, and automated shell spectrum analysis. Optimized for pseudo-spectral simulation auditing.