Exchange Laurent polynomial conjecture for generated period 1 seeds

Let $P=P(x_1,\cdots,x_{n-1})$ be an irreducible polynomial in the class used to generate the seed $\mathbf{(x,P)}$, and let $P_0$ be the initial exchange polynomial of that seed. A generated seed is assumed to have pseudoperiod $1$, meaning that $P_0=\tau_P(P_1)$. Exchange Laurent polynomial conjecture. If $\widehat{P}_0$ is the exchange Laurent polynomial of $P_0$ for the generated seed $\mathbf{(x,P)}$, then

$$\widehat{P}_0=P_0.$$

Together with the preceding proposition, this would show that period and pseudoperiod are equivalent for these seeds. The source gives no resolution of this conjecture.