No Edge to the Halo: KiDS-1000 Galaxy Lensing Against a Dark-Energy-Tied Gravity Framework's Cold Halos (Working Note)

Working note, version 1.0 (2026-10-16). AI-assisted research programme; not peer reviewed. In a gravity framework with a0 = (1/2) c sqrt(G rho_DE) (the 1/2 fitted), each galaxy's extra lensing mass is a collisionless 'cold' component settling onto the law g_N = g^2/(g + a0). Against the KiDS-1000 isolated-galaxy lensing rotation curves (Brouwer et al. 2021; 4 mass bins, full covariance) we test four pre-registered statements: (1) a halo truncated at the galaxy's own cosmic cold share (5.364 M_b, 5.84 r_M) is excluded (Delta chi^2 +197 within 0.31 Mpc, +753 all radii, both footings); (2) the framework's own collisionless infall, filling onto the law to 20-50 r_M, fits as well as an edgeless law (+0.1) if each galaxy draws on N >= 3-4 times its baryons; (3) N = 1/f_ret from the baryon census used in the framework's simulations (N ~ 6-10) fits within 0.31 Mpc with no fitted parameter (-0.2 / -1.5); (4) beyond each catchment edge the framework's own two-halo term from a 1024^3 simulation narrows the outer deficit from +149 to +11 (effective bias 0.2-0.5). Limits: the absolute fit is poor for every model including the plain law (chi^2 ~160/52), concentrated in the most massive bins (the known massive/early-type excess); the census supply is an observational input (a framework derivation failed); the two-halo simulation uses inherited initial conditions; one sigma_8 cross-check failed by 3.2%. AI assistance: Anthropic's Claude.