reasoning - Gauss’s law in 4+n dimensions with n dimensions compactified at radius R gives M_Pl^2 ~ M_^(2+n) R^n. Setting M_ ~ 1 TeV: n=1 requires R ~ 10^13 cm (solar-system-scale deviations, empirically excluded); n=2 gives R ~ 0.1-1 mm — allowed in 1998, since Newtonian gravity was untested below ~1 mm. So for n>=2 the construction is internally consistent with all then-existing gravity measurements, making a TeV fundamental scale viable rather than obviously excluded. Caveat carried in the paper itself: the radius must be stabilized at the large value, so the hierarchy is relocated rather than dissolved.
Verdict (step 6)
approved / checked. Traced the load-bearing step directly: Gauss’s law in 4+n dimensions gives V ~ 1/(M_^(n+2) r^(n+1)) at r<<R, matching onto 4D Newton at r>>R yields M_Pl^2 ~ M_^(2+n) R^n. Plugging M_* ~ 1 TeV: n=1 gives R ~ 10^13 cm (excluded by solar-system dynamics), n=2 gives R ~ 0.1-1 mm (untested in 1998). So the conclusion — a TeV fundamental scale is consistent with observed 4D gravity for n>=2 — follows, and the statement already carries the honest hedge that the hierarchy is relocated to radius stabilization, not solved. Undimmed by later torsion-balance limits: those bear on premise truth (priced in steps 7-8), not on the inference.