The Q-invariant and barred P-invariant generation conjecture for ${\rm Inv}_{R\overline{R}}$

Let $\operatorname{LSym}$ and $\overline{\operatorname{LSym}}$ be the loop symmetric-function rings, and set

$${\rm Inv}_{R\overline{R}}=\operatorname{Frac}(\operatorname{LSym})\cap\operatorname{Frac}(\overline{\operatorname{LSym}}).$$

Let the $Q$-invariants, barred $P$-invariants, and shape invariants $S_i$ be the invariants defined in the paper, together with their reduced versions.

Q-invariant and barred P-invariant generation conjecture. The field ${\rm Inv}_{R\overline{R}}$ is generated by the $Q$-invariants, barred $P$-invariants, and shape invariants. Every element of $\operatorname{LSym}\cap\overline{\operatorname{LSym}}$ is a polynomial in reduced $Q$-invariants, reduced barred $P$-invariants, and ratios $S_i/S_{i+1}$.

This is the symmetric counterpart to the conjecture for ${\rm Inv}_{R\overline{e}}$, exchanging the roles of the two loop-symmetric-function constructions. Its resolution is not supplied in the source.