Uniqueness of subsequential scaling limits for the two-dimensional KPZ equation

Let $u$, $\lambda$, and $D$ satisfy the effective-coupling condition from the paper, and let $(h^\varepsilon)_{\varepsilon>0}$ denote the rescaled KPZ fields, with $h^\varepsilon(t,\cdot)$ their time-$t$ spatial fields. Uniqueness of scaling limits conjecture. Under the condition defining the effective coupling constant, the sequences $(h^\varepsilon)_{\varepsilon>0}$ and $(h^\varepsilon(t,\cdot))_{\varepsilon>0}$ converge in law as $\varepsilon\to0$. The conjecture asserts uniqueness of the subsequential scaling limits whose existence is established in the paper; proving convergence of the full families remains open.