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) = κₑpi/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 rₘ = r₀ (1 ∓ √2/m) in the floor-dominated outer disk, and a generalised condition rILR/rOLR = (1 − KILR/m) / (1 + KOLR/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 rᵢnner/rₒuter 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 M > F confirmed across the full arm-classified S⁴G sample (chi-square p 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).