MultiscaleStatisticalPhysicsₒfModularCompressionSystems

We present a reproducible computational framework for analyzing modular compression systems over finite residue spaces Zₙ. The framework integrates information-theoretic observables, spectral analysis, scaling laws, renormalization group flows, and effective field-theoretic analog representations into a unified multiscale pipeline. Across multiple moduli, we compute entropy, Kullback--Leibler divergence, and spectral gap statistics while analyzing emergent invariance structures through embedding geometry and phase-transition-like behavior. Scaling analyses reveal partially stable cross-modular organization consistent with finite stochastic systems. No evidence of non-stochastic determinism is observed under null-model comparison. Instead, the framework establishes a rigorous computational methodology for studying discrete symbolic systems using tools derived from statistical physics, information geometry, and complex systems analysis.