The galaxy-scale gravitational lens B0128+437 generates a quadrupole-image configuration of a background quasar that shows milli-arcsecond-scale subcomponents in the multiple images observed with VLBI. As this multiple-image configuration including the subcomponents has eluded a parametric lens-model characterisation so far, we determine local lens properties at the positions of the multiple images with our model-independent approach. Using PixeLens, we also succeed in setting up a global free-form mass density reconstruction including all subcomponents as constraints. We compare the model-independent local lens properties with those obtained by PixeLens and those obtained by the parametric modelling algorithm Lensmodel. A comparison of all three approaches and a model-free analysis based on the relative polar angles of the multiple images corroborate the hypothesis that elliptically symmetric models are too simplistic to characterise the asymmetric mass density distribution of this lenticular or late-type galaxy. In addition, the model-independent approach efficiently determines local lens properties on the scale of the quasar subcomponents, which are computationally intensive to obtain by free-form model-based approaches. As only 40% of the small-scale subcomponent local lens properties overlap within the 1-$sigma$ confidence bounds, mass density gradients on milli-arcsecond scales cannot be excluded. Hence, aiming at a global reconstruction of the deflecting mass density distribution, increasingly detailed observations require flexible free-form models that allow for density fluctuations on milli-arcsecond scale to replace parametric ones, especially for asymmetric lenses or lenses with localised inhomogeneities like B0128.
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