Gaiotto–Johnson-Freyd trivialization conjecture for TQFT target categories

Let $\Sigma^{n-1}\mathsf{Vect}^{fd}$ and $\Sigma^{n-1}\mathsf{sVect}^{fd}$ be the stable suspensions used as codomains for bosonic and fermionic fully extended TQFTs, respectively. Their maximal $\infty$-groupoids carry canonical homotopy $SO(n)$- and $Spin(n)$-actions. Gaiotto–Johnson-Freyd conjecture. The canonical homotopy $SO(n)$-action, respectively $Spin(n)$-action, on these maximal $\infty$-groupoids is canonically trivializable. This is the same conjecture as the preceding attributed formulation, restated in the paper's summary; its resolution is not given in the source.