Gravity as a Primary Field (GPF): Cosmological Baseline and Galactic Fits

We present Gravity as a Primary Field (GPF), a minimal metric f (R) =R+alpha L² R² baseline whose weak-field limit is a linear Helmholtz/Yukawa sector with a single galactic scale lambda. The formulation is slip-free, so one and the same potential governs dynamics and lensing. Using public SPARC rotation curves with the full thin-disc Yukawa convolution, within a fully reproducible pipeline and fair per-galaxy model selection, a universal lambda is ruled out without a local modulator Q. With a mild Q (r; rq, p) the data are consistently described by a single lambda₀ ~ 10 kpc with a gentle turn-on p ~ 1. 5 and an empirical width-scale relation rq ~ kappa * Rdˢ (kappa ~ 0. 25, s ~ 0. 56). We pre-register decisive checks and falsification targets (inner/outer radial hold-outs, parity against NFW/ISO at matched degrees of freedom, hierarchical global-lambda tests with and without Q, Solar-System/PPN and lensing consistency, a predictive Q-onset relation r50/Rd = kappa * Rd^ (s-1) / (2^ (1/p) - 1), and robustness to known systematics such as distance, inclination, non-circular motions, M/L_* priors, and disc thickness). Interpretively, at galactic scales GPF reframes dark-matter ("black matter") halo phenomenology as effective geometry: a geometry-fixed, mass-like Q allows one slip-free potential to account for rotation curves and remain lensing-consistent without introducing a new substance. Extending this replacement beyond galaxies (clusters, CMB, and large-scale structure) or falsifying it remains an open test program.