Spectral Slope Branch Structure and Observational Localization in a Constraint-Driven Non-Equilibrium Update System

This record contains the manuscript, figures, and processed datasets associated with the study: "Spectral Slope Branch Structure and Observational Localization in a Constraint-Driven Non-Equilibrium Update System". The study investigates spectral slope structures generated by a constraint-driven non-equilibrium update system. Numerical simulations reveal the presence of multiple spectral slope branches arising from non-commutative coarse-graining dynamics. The statistical distribution of spectral slopes produced by the model is compared with the observed spectral slope derived from the CMB angular power spectrum. A related study identified a critical transition in the same update system (Furuya, 2026), providing the parameter regime in which the spectral slope branch structure emerges. The analysis shows that the observational CMB spectral slope lies within the structural phase space generated by the model, specifically within the transition region between slope branches. The record includes the manuscript, figures used in the study, and processed datasets used in the slope comparison. Related work:Critical Transition and Reliability Boundary...https://doi.org/10.5281/zenodo.18986867