The pole conjecture for eigenvectors of Lannes' T-functor

Let $K^{red}(\mathcal U)$ be the Grothendieck ring of finite direct sums of indecomposable reduced injective unstable modules, and let $v$ be a virtual module in $K^{red}(\mathcal U)$ that is an eigenvector for Lannes' $T$-functor with eigenvalue $1$. Let $P_v(q)$ denote its Poincaré series. Pole conjecture. The Poincaré series of each eigenvector for $T$ associated to the eigenvalue $1$ has no pole at $1$. The source says that this is supported by numerical evidence and does not report a proof or disproof.