Trivial LGBs are associated with pre-classical theories

Let $\mathcal{G} \to M$ be a trivial LGB over a spacetime $M$ such that its LAB $\mathcal{g}$ admits an $\mathrm{Ad}$-invariant fibre metric $\kappa$, and let

$$\mathcal{P} \stackrel{\pi}{\to} M$$

be a principal $\mathcal{G}$-bundle. Let $\mathrm{H}\mathcal{G}$ be a Yang–Mills connection on $\mathcal{G}$, and let $A \in \Omega^1(\mathcal{P};\pi^*\mathcal{g})$ be a connection 1-form on $\mathcal{P}$.

Trivial LGBs are associated with pre-classical theories. There exists a $\lambda \in \Omega^1(M;\mathcal{g})$ such that $\widetilde{\nabla^{\mathrm{YM}}}^{\lambda}$ is flat.

This conjecture asserts that curved Yang–Mills theories based on trivial LGBs can be transformed by a field redefinition into theories with flat Yang–Mills connection, namely pre-classical theories. The source gives no resolution of the conjecture.