Accessibility Hierarchy of Galaxy Rotation Curves Reveals Four Dynamical Regimes and an Empirical Ordering Field in the SPARC Sample

Building upon the hydrogen-equivalent ordering framework established in a companion manuscript (Moslemi Tabrizi, 2026, submitted), we present an accessibility-hierarchy analysis of galaxy rotation curves applied to 71 galaxies (1166 rotation-curve points) drawn from the SPARC database. The regime boundaries at H = 1, 4, and 8 are not chosen empirically; they follow from the C⁸ mass-scaling hierarchy of the companion framework, in which galactic dynamical mass is proposed to organize around stability scales analogous to the nuclear binding-energy sequence that rises from hydrogen toward a maximum near iron before declining for heavier nuclei. This nuclear-stability analogy concerns only this structural energy-binding pattern, not any literal atomic, isotopic, or chemical reconstruction at galactic scale. Introducing a dimensionless hydrogen-equivalent ordering parameter Hₑᵧᵩᵥ, we find evidence that the SPARC residual field is not randomly distributed but is consistent with four statistically distinguishable dynamical regimes: a hydrogen-dominated stable branch (Regime I, H < 1), an intermediate stable branch (Regime II, 1 ≤ H < 4), a bifurcated transition region (Regime III, 4 ≤ H < 8), and a high-H stable branch (Regime IV, H ≥ 8). The transition regime further separates into two sub-branches, IIIA (xₘₐₓ < 10.5, χ² ≈ 5.18) and IIIB (xₘₐₓ ≥ 10.5, χ² ≈ 7.01), where IIIB concentrates the dominant fraction of residual complexity across the entire sample. A global signed accessibility correction Vₙᵉʷ = Vᶜᵒᴿᴿ + AΦₐᶜᶜ, with a single coefficient A = 96.09 ± 1.80 km s⁻¹ determined from Bayesian inference, achieves a global χ² ≈ 2.14 and a median point-level χ² ≈ 0.225 without any galaxy-by-galaxy parameter optimization. Compared with standard benchmark descriptions, the framework yields ΔAIC ≈ 510 over NFW, ΔAIC ≈ 1338 over Burkert, and ΔAIC ≈ 6710 over MOND, with win fractions of 53.5%, 57.7%, and 85.9% respectively on a galaxy-by-galaxy basis. Independent validation through Markov Chain Monte Carlo exploration, five-fold cross-validation, full Gaussian likelihood analysis, and information-criterion diagnostics consistently confirms the statistical identifiability of the accessibility coefficient. The residual structure is interpreted as evidence for an accessibility ordering field whose local manifestations define the four regimes while a single global law connects them. The localization of residual stress within the IIIB transition branch provides a physically motivated roadmap for future model refinement. Connections between the galactic accessibility hierarchy and cosmological activation layers are noted as a direction for subsequent investigation.