Equality of abelian and Artin–Schreier ramification functions

Let $L/K$ be an extension of complete discrete valuation fields, and let $k$ be the residue field. Assume that $k$ is perfect of characteristic $p>0$.

Equality conjecture. The two generalized ramification functions satisfy

$$\psi^{\mathrm{ab}}_{L/K}=\psi^{\mathrm{AS}}_{L/K}.$$

The functions are proposed as generalizations of the classical

$$\psi$$

-function; the paper's preceding results provide evidence for their equality, but the claim is not resolved in the supplied text.