Uniqueness conjecture for connected well-indumatched graphs of girth 11

Let $G$ be a connected well-indumatched graph of girth $11$, and let $C_{11}$ denote the cycle on $11$ vertices. The girth-11 uniqueness conjecture. The cycle $C_{11}$ is the only connected well-indumatched graph of girth $11$. This would settle the only remaining girth case not covered by the paper's dichotomy: for every other girth at least $3$, the authors either prove nonexistence or construct an infinite family of well-indumatched graphs. The conjecture remains open here; the paper establishes only that $C_{11}$ is the sole minimal well-indumatched graph of girth $11$.