Phase-Window Access as a Dynamic Formulation Discriminator during Reheating

This paper studies formulation-dependent access to the moving Phase-IV reheating window in the dynamic reheating phase framework. Even with a common Jordan-frame seed, metric and Palatini formulations generate different Einstein-frame effective histories and therefore different trajectories in complex reheating phase space. The difference is quantified by onset shift, boundary displacement, and access efficiency, which together define a dynamic formulation discriminator. V2: This version upgrades the manuscript from a conceptual framework to an explicit result. A minimal formulation-dependent benchmark model is introduced, in which metric and Palatini trajectories are computed from a common Jordan-frame seed under a controlled deformation of the effective reheating history. The dynamic observables are reformulated in a numerically stable manner using a regularized logarithmic-derivative prescription and a coarse-grained access curve. The main result is now demonstrated explicitly: the two formulations produce distinct access curves, a nonzero onset displacement ΔuIV(P−M)(R∗)\Delta u_{\rm IV}^{(P-M)}(R_*)ΔuIV(P−M)(R∗), and a nonzero access-efficiency gap ΔE(P−M)(R∗)\Delta E^{(P-M)}(R_*)ΔE(P−M)(R∗) over a finite threshold range. A robustness scan in the (cP,R∗)(c_P, R_*)(cP,R∗) plane shows that the sign of the onset displacement remains stable across a finite domain of formulation deformation. An analytic estimate is also provided, showing that the onset shift is controlled by the relative decay rates of the effective amplitude and phase-rotation histories, explaining the origin and sign of the discriminator. As a result, the moving Phase-IV boundary is no longer only a conceptual construct but functions as an operational formulation discriminator once the dynamic framework is closed by an explicit reheating history.