Moduli tracking conjecture under involutive mutation

Let $I$ be the index set and let $M$ be the module in the moduli-tracking setup. Let $\upnu_I$ denote mutation at $I$, and assume $\upnu_I\upnu_I M\cong M$. Moduli tracking conjecture. The moduli tracking theorem stated in the paper is true under the simplifying assumption $\upnu_I\upnu_I M\cong M$. The claim is motivated by examples in which the double mutation condition holds; the source gives no general proof.