Genus 9 and 11 minimal stretch factor conjecture for nonorientable surfaces

Let $N_g$ be the closed nonorientable surface of genus $g$, and let $\delta^+(N_g)$ be the minimal stretch factor among pseudo-Anosov homeomorphisms of $N_g$ with an orientable invariant foliation. The singularity type records the prong numbers of the singularities of a minimizing pseudo-Anosov map.

Genus 9 and 11 minimal stretch factor conjecture. The minimal stretch factors and minimal polynomials are predicted to be

$$\begin{array}{c|c|c|c} g & \delta^+(N_g)\approx & \text{Minimal polynomial of }\delta^+(N_g) & \text{singularity type}\\ \hline 9 & 1.35680 & x^8-x^5-x^4-x^3-1 & (16)\\ 11 & 1.22262 & \dfrac{x^{12}-x^7-x^6-x^5-1}{x^2+x+1} & (8,8,8) \end{array}$$

These predictions concern the cases not settled by the paper's elimination tests: the authors state that the remaining candidate polynomials should be eliminable and that their constructed examples should be minimal. The conjecture is open in the source.