Resonance Ring Geometry of Disk Galaxies from an 3-Sphere Acceleration Floor

This record contains the complete source package for the paper Resonance Ring Geometry of Disk Galaxies from an S³ Acceleration Floor (Banasik 2026). The S³ acceleration floor a* = c²/πR — the potential gradient of a closed three-sphere of cosmic radius R — forces asymptotically flat rotation curves, which in turn fix the epicyclic-to-orbital frequency ratio K(r) = κ_epi/Ω → √2 in the outer disk. Applying the Lindblad resonance condition to the full radial K(r) profile derived from the two-channel master formula yields a parameter-free resonance spectrum r_m = r₀(1 ∓ √2/m) in the floor-dominated outer disk, and a generalised condition r_ILR/r_OLR = (1 − K_ILR/m)/(1 + K_OLR/m) in the inner disk. Flat rotation curves, ring resonance structure, and galactic shells are shown to share a single geometric origin in a* = c²/πR. Observational tests Three nested tests are reported at increasing sample size using publicly available S⁴G catalogs (Comerón et al. 2014; Buta et al. 2015; Salo et al. 2015): Level 1 (N = 112): ring ratio r_inner/r_outer tested against ARRAKIS ring radii × Elmegreen arm classifications. Flocculent galaxies (m = 4) consistent with the floor prediction at p = 0.99; deviations for grand-design galaxies explained by K < √2 in the inner disk, confirmed by a ring-size gradient at Spearman ρ = −0.50 (p < 0.0001). Level 2 (N = 1,112): outer ring presence ordering G > M > F confirmed across the full arm-classified S⁴G sample (chi-square p < 0.0001), with Hubble-type confound discussed. Level 3 (N ≈ 1,000): bar strength ordering G > M confirmed (p < 0.001); G ≈ F inconclusive due to late-type barred irregulars; reported honestly. This paper is the third in the Wave Theory series. Companion papers: GOGD (Zenodo 10.5281/zenodo.20140822) and Physical Constants (Zenodo 10.5281/zenodo.20385871).