A Morphology-Specic Operator Family for Disk-Galaxy Kinematics: From Proxy Phenomenology toward a Class-Conditioned Field Response

We introduce a morphology-specic operator family for disk-galaxy kinematics and validate it on an independent, overlap-free fresh-only population (Pop C). The operator is constructed from the local residual structure of observed-minus-baryonic rotation curves, decomposed into radial windows normalised by the disk scale length. A bounded weighting search over these windows, applied separately per morphological class on Pop C, yields two empirically supported regimes: (i) an innermiddle suppression channel for low-surface- brightness (LSB) galaxies, S⋆ LSB = 0.5 ⟨|O|⟩inner + 0.5 ⟨|O|⟩middle, with a median non-isolated/isolated ratio of 0.527 and Cli's δ=−0.500; and (ii) an outer enhancement channel for normal disk galaxies, S⋆ disk = ⟨|O|⟩outer, with a ratio of 1.983 and Cli's δ= +0.289. A minimal forward model Vobs(R)−Vbar(R) = αOclass(R), using a single global coupling αper class and no galaxy-specic freedom, improves the baryons-only residual channel (LSB: R2 from 0.330 to 0.510; disk: R2 from 0.437 to 0.550). A bidirectional holdout test conrms that the LSB channel generalises out-of-sample. Bulge-dominated systems do not form a coherent single global class under the same architecture; however, a diagnostic subclass decomposition reveals an environment-modulated, negatively coupled bulge-core channel that remains positive under leave-one-galaxy-out validation at the level of predictive gain. The data therefore support a class-conditioned operator family whose morphology-specic structure reduces the baryonic residual channel in a nontrivial and independently tested manner