Kim–Rashkovskii's valuative invariance conjecture for Monge–Ampère masses

Let $\varphi$ and $\psi$ be plurisubharmonic germs with isolated singularities at $0\in\mathbb{C}^n$. For every divisorial valuation $v$ centered at $0$, write $v(\varphi)$ for its generalized Lelong number on $\varphi$, and let $e_n(\varphi,0)$ denote the residual Monge–Ampère mass at $0$. Kim–Rashkovskii's conjecture. If

$$v(\varphi)=v(\psi)$$

for every divisorial valuation $v$ centered at $0$, then

$$e_n(\varphi,0)=e_n(\psi,0).$$

In other words, the conjecture asserts that residual Monge–Ampère masses are valuative invariants of plurisubharmonic singularities. It is proposed by Kim and Rashkovskii, and the source gives no resolution.