Generic nonvanishing conjecture for the variational-equation Galois parameters

Let $\lambda$ and $E$ be the parameters of the axisymmetric Bianchi IX cosmological model, and let $\gamma_1,\gamma_2\in\mathbb{C}$ be the constants appearing in the differential Galois action on the variation-of-parameters integrals. Generic nonvanishing conjecture. Generically for $\lambda$ and $E$, $\gamma_1$ and $\gamma_2$ are not simultaneously zero. This assumption is used to ensure that the normal unipotent subgroup in the differential Galois group is nontrivial in the generic case, supporting the claimed non-integrability analysis.