Constraints on the underlying gravitational potential imposed by the variable inner slope fits. Top panel: Diagnostic diagram, equivalent to Fig. 5 for the polytropic fits, which includes all galaxies together. Note that around half of the galaxies have unphysical f < 0 irrespectively of the inner slope of the potential (c_p), a percentage that increases as r_s/r_sp increases. This is mostly due to the inner slope, c, being negative for a number of galaxies. Middle panel: Same as the top panel but including only good fits (Relative RMS < 0.02). Note how the fraction of unphysical potentials with f < 0 has been significantly reduced (the tone becomes bluish rather than greenish). Bottom panel: Same as the top panel but including only low-mass galaxies (M_⋆< 10⁷ M_⊙). As expected, the fraction of potentials with f < 0 increases (the tone becomes reddish) due to the increase in fits with c< 0. The color bar shows the percentage of galaxies with f ≥ 0.