Liechti–Strenner's minimal dilatation conjecture for closed nonorientable surfaces

Let $N_g$ be the closed nonorientable surface of genus $g$, and let $[+]{\delta}^{+}(N_g)$ denote the minimal dilatation among pseudo-Anosov diffeomorphisms of $N_g$ with an orientable invariant foliation. For each integer $k\geq 2$, let $r_k$ be the largest real root of

$$x^{2k-1}-x^k-x^{k-1}-1.$$

Liechti–Strenner's conjecture. For all $k\geq 2$,

$$\delta^{+}(N_{2k})=r_k.$$

Liechti and Strenner determined this minimal dilatation for several even genera, including $4,6,8,10,12,14,16,20,24,28,32,36$ and $40$; the conjecture predicts the formula for every even genus at least $4$.