McDuff's restricted stabilized ellipsoid embedding conjecture

Let $E(a,b)$ denote the four-dimensional symplectic ellipsoid, let $B^4(c)=E(c,c)$ be the round four-ball, and for $N\in\mathbb{Z}_{\geq 1}$ define

$$f_N(x):=\inf\\{c\in\mathbb{R}_{>0}:E(1,x)\times\mathbb{C}^N\overset{s}\hookrightarrow B^4(c)\times\mathbb{C}^N\\}.$$

Also let $f_0(x)$ be the corresponding unstabilized embedding function, and let $\tau$ denote the golden ratio. McDuff's restricted stabilized ellipsoid embedding conjecture. For $x\in\mathbb{R}_{\geq 1}$ and $N\geq 1$,

$$f_N(x)=\begin{cases} f_0(x)&\text{if }x\leq\tau^4,\\\\ \dfrac{3x}{x+1}&\text{if }x>\tau^4.\end{cases}$$

This conjecture specifies the stabilized embedding function when the target is a stabilized round four-ball, extending the four-dimensional Fibonacci-staircase problem. Its resolution status is not specified in the source.