The trace formula conjecture for multilinear representations of free PROs

Let $\mathcal T$ be the free PRO under consideration, let $\mu$ be a representation of $\mathcal T$ of dimension $N$, and let $d$ denote the parameter appearing in the trace of the elementary generator. For a diagram $\mathfrak d\in\mathcal T\ell_n$, write $\mathrm{triv}(\mathfrak d)$ and $\mathrm{ntriv}(\mathfrak d)$ for the associated diagram statistics. Trace formula conjecture. For every $\mathfrak d\in\mathcal T\ell_n$,

$$\mathrm{tr}(\mu(\mathfrak d))=N^{\mathrm{triv}(\mathfrak d)}d^{\mathrm{ntriv}(\mathfrak d)}.$$

This conjecture generalizes the preceding trace computations for elementary and separated diagrams, proposing a uniform formula for all diagrams in the free PRO. The supplied text does not state whether the formula has been proved or disproved.