The odd-genus Penner dilatation limit conjecture

Let $N_g$ be the nonorientable closed surface of genus $g$, and let $\delta_P(N_g)$ denote the minimal dilatation among pseudo-Anosov homeomorphisms arising from Penner's construction on $N_g$. The odd-genus limit is

$$\lim_{k\to\infty}\delta_P(N_{2k+1}).$$

Odd-genus Penner dilatation limit conjecture. The limit is the largest real root of

$$x^4-8x^3+13x^2-8x+1,$$

approximately $6.071360241468951$. The preceding theorem establishes only that this limit exists and is greater than $3+2\sqrt{2}$; the stated value is suggested by computations and remains open.