Universal Nonminimal Coupling-to-Starobinsky Matching and a Single-Field Attractor

We establish an off-shell commutativity theorem in 4D parity-even quadratic gravity that the Hubbard-Stratonovich/Legendre lifts, algebraic elimination of auxiliaries, including the torsionless Palatini connection, and Jordan-Einstein Weyl rescalings commute at the action level up to boundary terms. This yields a frame-independent characterization of the propagating degrees of freedom and isolates a universal scalaron EFT in the metric branch, while clarifying the algebraic nature of the Palatini $f(R)$ scalar. We obtain, as a result, a frame-universal matching from the generic nonminimal couplings to a positive $R^2$ sector and a quantitative single-field attractor bound, enhanced by a $1\mathrm{/}\mathrm{\Delta }N$ selection term, providing sharp and falsifiable CMB targets.