The following statements are made in a recent paper (Takada et al. PRL, 113 (2014) 1266101): "...unexpected results have been obtained for the phase shift in the Kondo regime...: for instance ...  in the Kondo valley [between two resonances]. ...Explanations of these surprising features are still lacking." Earlier papers in PRB 61, 2716 (2000); 74, 115328 (2006) by A. Yahalom and myself  showed how the gate voltage variability of the phase can  be uniquely obtained from the corresponding current intensity.  The log of the latter and the phase are Hilbert transforms (of each other), in the same way as are the real and imaginary parts of e.g., the frequency dependent dielectric constant,  exemplified by the Kramers-Kronig relations - and for the same reasons: causality and the consequent analyticity in the complex frequency/gate voltage plane.

Using  the Hilbert transformation method  I have now reconstructed the phase vs. gate voltage curves of Takada et al from their current intensity (I₂) as the only numerical input in the integration and with no adjustable or fitting  parameters (excepting the subtraction of a linear background). 

I have also obtained for the first time a simple criterion for the phase slope at the midpoint of the valley between the resonances, exclusively from elementary parameters of the resonance (intensity) shapes.