Planetary Spacing and Galaxy Rotation: The Titius-Bode Doubling and the Tully-Fisher Fourth Power, Forced

One axiom. One operation. Zero free parameters. Two empirical laws of the sky, long known but never derived: the Titius-Bode planetary spacing (each orbit ~twice the last) and the Tully-Fisher relation (galaxy luminosity ∝ rotation speed to the fourth power). This paper forces both. Planetary spacing is the binary tower: stable orbital resonances are fold orbits with spacing a_n ∝ a₀·2ⁿ, each orbit doubling the last, the forced ratio 2 being the fold’s base. Galaxy rotation’s fourth power is the fold’s radiation/spacetime exponent: the 4 = d+1 (three spatial dimensions plus one), the same 4 that governs radiation dilution (a⁻⁴), so L ∝ v⁴. Two laws of the heavens, one fold base and one dimensional exponent. The same module ties the galactic dark sector to the covering ratio 27/5. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory