Critical Proxy Strength and Formulation-Switching Cartography in Reduced Reheating Geometry

This repository contains the manuscript, figures, and numerical scan data for the paper: “Critical Proxy Strength and Formulation-Switching Cartography in Reduced Reheating Geometry” The paper extends the fixed-cPc_PcP formulation comparison of the preceding work to a threshold-level cartography over the reduced reheating plane (α,β)(\alpha,\beta)(α,β). The central object is the critical proxy strength cP∗(α,β)=min⁡{cP:σmin⁡(JP)(cP;α,β)>σmin⁡(JM)(α,β)},c_P^*(\alpha,\beta) = \min\{c_P : \sigma_{\min}(J_P)(c_P;\alpha,\beta) > \sigma_{\min}(J_M)(\alpha,\beta)\},cP∗(α,β)=min{cP:σmin(JP)(cP;α,β)>σmin(JM)(α,β)}, defined as the minimum proxy strength at which the Palatini formulation becomes observationally advantaged over the metric one under the smallest-singular-value criterion. The main results are: A sign-level cartography showing how the Palatini-advantaged region expands as cPc_PcP increases. A critical-threshold map cP∗(α,β)c_P^*(\alpha,\beta)cP∗(α,β) over the reduced reheating plane. Identification of a finite-threshold sector occupying about 23% of the scanned domain. Within that finite-threshold sector, about 86% of points satisfy cP∗<1.3c_P^* < 1.3cP∗<1.3, with median threshold cP∗=1.1c_P^* = 1.1cP∗=1.1. Evidence that formulation switching is not uniformly distributed, but instead forms a localized and coherent low-/intermediate-α\alphaα sector, while a broad high-α\alphaα region remains a no-switch sector within the scanned range. In this sense, the paper promotes the single-slice comparison of the previous work to a full threshold cartography of formulation switching in reduced reheating geometry. Files in this deposit include the manuscript source, compiled PDF, figure files, and the numerical scan archive used to construct the threshold map and associated statistics. V2: corrected and extended formulation-switching cartography in reduced reheating geometry. The update fixes the Palatini-advantage threshold condition, introduces explicit invalid/no-switch separation in the critical map, and clarifies the discrete first-passage interpretation of cP∗(α,β)c_P^*(\alpha,\beta)cP∗(α,β). Additional robustness diagnostics include local recomputation tests, tolerance sensitivity checks, sign-flip audits, and finite-difference / ODE-resolution sensitivity analyses supporting the stability of the large-scale tripartite switching geography.