Jara's conjecture on KPZ mixing for particle-conserving systems

Consider a particle-conserving system on a ring of size $N$ with only nice local interactions, and let the average current be a function of the particle density. Assume that the second derivative of the average current does not vanish. Jara's mixing-time conjecture. The mixing time is of order $N^{3/2}$, up to poly-logarithmic corrections. This conjecture proposes the same characteristic mixing scale beyond exclusion processes, but the source provides no resolution and leaves the assertion open.