The Hubble-Kernel Growth Equation: A Parameter-Free, Falsifiable Late-Time Growth Law from a de Sitter-Locked MOND Scale

If the galactic acceleration scale is locked to the dark-energy density, a0 = κ c sqrt(G ρΛ), and the MOND kernel on cosmological scales sees the Hubble-flow acceleration cH(z) as its ambient field (the only prescription surviving a lensing test in the accompanying repository), the effective gravitational coupling of linear structure is fixed with no new parameter: Geff(z)/G = ν(cH(z)/a0) with (cH0/a0)2 = 8π/(3κ2ΩΛ) = 49 for κ = 1/2, i.e. cH0/a0 = 7.0, with ν the radial-acceleration-relation function. Predictions: Geff/G = 1.077, 1.050, 1.030, 1.004 at z = 0, 0.5, 1, 3; σ8 raised by 1.1% (1.5% alternative footing) over Planck-ΛCDM, S8 = 0.843 (0.847); fσ8 raised by 2.7%, 1.9%, 1.1% at z = 0.3, 0.6, 1.0. Sign opposite to the S8 tension; inside current RSD errors; at DESI full-sample reach. Identity machine-checked in Lean 4; growth computation a committed script. Falsifiable by a low-S8 or low-fσ8 result at the few-percent level. AI-assisted research programme; not peer reviewed.