Exact minimal normalized stretch factor conjecture for orientation-reversing fully-punctured pseudo-Anosov maps

Let $f:S \to S$ be an orientation-reversing fully-punctured pseudo-Anosov map on a finite-type orientable surface. Suppose $-\chi(S)=2k\geq 4$ and $f$ has at least two puncture orbits.

Exact minimal stretch factor conjecture. The normalized stretch factor of $f$ is greater than or equal to the largest real root of

$$\begin{cases} t^{2k}-t^{k+1}-t^{k-1}-1 & \text{if $k$ is even},\\ t^{2k}-t^{k+2}-t^{k-2}-1 & \text{if $k$ is odd.} \end{cases}$$

Equivalently, the examples demonstrated in the paper should attain the minimal normalized stretch factor among orientation-reversing fully-punctured pseudo-Anosov maps on surfaces with even Euler characteristic and at least two puncture orbits. The conjecture is motivated by the fact that the main theorem determines only the asymptotic minimum; verifying it would require extending the curve-graph analysis to more cases, and the necessary classification and polynomial analysis remain incomplete.