Structural Governance of Gas Pressure Support in Galactic Disks: A Two-Variable Scaling Relation Linking Rotational Organization and Radial Structure

The balance between ordered rotation and pressure support is a central feature of gaseous galactic disks, yet a one-variable measure such as V/σ does not fully describe how that balance changes within individual galaxies. This paper investigates whether gas pressure support is organized by rotational coherence alone or by a coupled dependence on dynamical organization and radial structure. The rotational organization parameter is defined as R_org = (V_rot/σ)², and the fractional pressure-support measure as F = (V_c² − V_rot²)/V_c². Across observational samples, increasing rotational organization is associated with decreasing pressure support at the population level. A candidate transition near R_org ≃ 84 successfully identifies highly organized systems in an independent WHISP holdout sample, but it fails as a universal physical boundary when tested against regular, low-R_org H I disks. Radially resolved LITTLE THINGS data further show that a one-variable local relation between F and R_org cannot describe all galaxies: the sign of the within-galaxy trend varies from system to system. Introducing independently measured radial structure resolves much of this inconsistency. For the primary resolved sample, F/(1−F) ∝ R_org^−0.91(r/R_d)^1.82, with R² ≃ 0.87 when galaxy-specific normalization is allowed. Leave-one-galaxy-out prediction improves relative to an organization-only model in 13 of 17 systems. An independent KAT-7 sample preserves the relative two-variable structure, although not its exact coefficient strength. Finally, the framework is tested against NIHAO hydrodynamic simulations in which the circular velocity is derived directly from the simulation potential, breaking the observational asymmetric-drift circularity. The locked two-variable predictor retains the expected positive direction in all four simulated galaxies and improves prediction relative to R_org alone. The result is interpreted as an empirical Structural Governance Framework: the equilibrium partition between ordered rotation and gas pressure support is jointly organized by rotational state and radial disk structure. The relation is not presented as a universal fundamental law or immutable constant