Physical interpretation of the empirical omega diagnostic

Determine the physical interpretation of the empirical two-boundary kinematic correction parameterized by \(\omega\) for baryonic rotation-curve reconstruction in the 84-galaxy SPARC benchmark.

Background

The paper evaluates an empirical transformation that computes a single coefficient $\omega$ from the innermost and outermost measured points of each galaxy’s observed rotation curve, then transforms the full profile according to $V_{\rm adj}=V_{\rm obs}-R\omega$. The analysis validates this procedure as a reproducible data transformation and diagnostic, but explicitly avoids assigning it a new force law or a unique cosmological interpretation.

Although the transformed curves are compared with baryonic reconstructions and show reduced aggregate discrepancies relative to a simple Keplerian reference, these numerical results do not establish the physical mechanism underlying $\omega$. The unresolved issue is therefore to identify and substantiate what physical phenomenon, if any, the empirical correction represents.