The asymptotic scaling conjecture for the volume loss function

For $L,R>0$, let

$$\mathrm{VL}(L,R):=\inf\left\{\operatorname{Vol}({E}(\Phi)): \Phi\colon B^{4}(\pi R^2)\to\mathbb{R}^4\text{ is a symplectic embedding with Lipschitz constant at most }L\right\},$$

where

$${E}(\Phi)=\Phi^{-1}(\mathbb{R}^{4}\setminus Z^{4}(\pi)).$$

Volume-loss scaling conjecture. For any $\ell,r>0$, the limit

$$\lim_{R\rightarrow\infty}\lim_{L\rightarrow\infty}\frac{\mathrm{VL}(\ell L,rR)}{\mathrm{VL}(L,R)}$$

exists and is positive. This conjecture concerns the relation between the known upper and lower bounds for volume loss and the asymptotic dependence on the Lipschitz and radius parameters; the supplied text gives no resolution.