Dynamic Saturation Boundary in the Universal Reheating Phase Diagram of Axion Initial Data

This repository contains the source files for a paper that generalizes the universal reheating phase diagram of axion initial data to the case of temperature-dependent axion mass. The work shows that thermal mass evolution turns the fixed saturation boundary of the static theory into a moving boundary, deforms the previously identified Phase-IV diagnostic window, and compresses the surviving phase-sensitive information into a narrow filamentary structure in effective-data space. V2: This version refines the presentation and internal consistency of the dynamic reheating-phase framework. Section references and figure consistency have been corrected throughout, including the benchmark parameter labeling in the diagnostic plots. The leading-order treatment of the time-dependent axion mass is now stated more precisely, and the moving saturation boundary is defined more clearly as a transition band in the phase-diagnostic regime. The benchmark parametrization has also been clarified, with the coarse-grained roles of κ\kappaκ, αH\alpha_HαH, and β\betaβ stated explicitly. In addition, the diagnostic and geometric figures have been revised to distinguish exact quantities from visualization proxies, especially for the envelope-level amplitude suppression and the phenomenological spaghettification indicator. These changes do not alter the central result: temperature-dependent axion mass promotes the static saturation separator into a moving, history-dependent diagnostic boundary with a surviving phase-sensitive channel. v3:Introduces a dynamic extension of the universal reheating phase framework for axion initial data by incorporating temperature-dependent mass. The saturation boundary becomes a history-dependent moving structure driven by accelerated phase accumulation. The Phase-IV diagnostic window is deformed but persists, and a minimal Jacobian realization shows anisotropic compression (spaghettification) of initial-data distributions.