Deformation Modes of Fold Discriminants in Reduced Reheating Geometry: Observable-Space Displacement Direction as a Primary Classification Signal

This work develops the deformation theory of fold-governed branch interfaces in reduced reheating geometry. Building on the identification of fold singularities as the leading organization principle of reduced inverse ambiguity, the paper analyzes how the fold discriminant and its normal covector respond when the underlying reduced observation map is perturbed away from a baseline power-law normal form. Two minimal non-power-law perturbations are introduced: (i) a phase‑biased frequency drift that primarily affects the cumulative‑phase observable, and (ii) an onset‑biased amplitude drift that primarily affects the onset‑ and efficiency‑type observables. Using singular‑value cartography, observable‑space proxy displacement, and normal‑covector weight analysis, the paper shows that the two deformation modes separate most clearly by the direction of observable‑space displacement: the phase‑biased mode is predominantly Δθ‑directed (normal‑rotation‑favoring), the onset‑biased mode is predominantly u\_IV/E‑directed (interface‑shift‑favoring). Both modes exhibit non‑negligible mixed behavior in their normal‑weight response, indicating that deformation classification is comparative rather than absolute. The results establish a first‑order deformation theory of fold discriminants in reduced reheating geometry and identify the first geometric precursors of higher‑codimension onset (such as cusp formation) as secondary effects beyond leading fold deformation. V2: clarified the distinction between exact fold-discriminant geometry and finite-resolution proxy geometry, added robustness checks for onset interpolation and normalization choices, unified the operational near-fold definition (σfold=0.185\sigma_{\rm fold}=0.185σfold=0.185), and refined the displacement/reorganization taxonomy using estimator-based diagnostics.