WP3: First Empirical Slice Through the Regime Response Surface R(k, S)

We present the first empirical mapping of the regime response surface R(k,S)R(k,S)R(k,S) along the redshift-space distortion (RSD) trajectory. Using fσ8(z)f\sigma_8(z)fσ8​(z) measurements from BOSS DR12, eBOSS DR16, and DESI Y1 (N=12N=12N=12), we constrain one coordinate on the gravitational response surface: R(k≈0.13h/Mpc,S≈0.30)≈+0.30R(k \approx 0.13\,h/\mathrm{Mpc}, S \approx 0.30) \approx +0.30R(k≈0.13h/Mpc,S≈0.30)≈+0.30. Under Akaike Information Criterion (AIC), Λ\LambdaΛCDM (R=0R=0R=0) is preferred by ΔAIC=−3.8\Delta\mathrm{AIC} = -3.8ΔAIC=−3.8, indicating that the data are consistent with zero response once model complexity is penalized. The structural maturity variable SSS is implemented here via a monotonic proxy mapping and should be replaced in future work with observables derived from nonlinear growth statistics. The response profile μ(z)\mu(z)μ(z) is modeled using a phenomenological basis function, not a theoretical prediction.This work represents cartography—a measurement in a new coordinate system—rather than model validation or falsification. WP3 provides the first entry in a planned response atlas mapping gravitational behavior across structural regimes.