No Late-Time Step in Newton's Constant from Extra Dimensions, and the Screening Requirements of the Scale-Invariant Loophole

A sharp ~4% increase in Newton’s constant at redshift z ≈ 0.01 (the “G step”) has been proposed to resolve the Hubble tension, but no physical mechanism for it is known. We show that extra-dimensional compactifications cannot supply one. If G is controlled by a stabilized modulus, the transition shifts the four-dimensional vacuum energy at first order in ΔG/G, by at least 10^58 times the observed dark-energy density. The coefficient is exactly 1/3 in an explicit 6D Einstein–Maxwell flux compactification, and the bubble-wall and brane-induced-gravity alternatives fail independently. The only escape is a light modulus. In a classically scale-invariant 6D bulk this gives a Brans–Dicke scalar with ω = 1/2, a fifth force of strength α = 1/4 fixed by geometry. Unscreened, it violates the Cassini bound, so the G step becomes a screening problem. We derive quantitative requirements that any screening mechanism (a “dilaton brake coupling”) must meet and show that known mechanisms fail them. In the allowed window H0 ≈ 69–70 km/s/Mpc, so this route can at most ease the Hubble tension. Preprint; not yet peer reviewed.