The parallel-source conjecture for classical de Sitter solutions

Let a classical de Sitter solution be a solution of the ten-dimensional theory with sources consisting of orientifold planes $O_p$ and D-branes $D_p$. The sources are parallel when they extend along the same dimensions of the ten-dimensional spacetime.

Parallel-source conjecture. There is no classical de Sitter solution with parallel sources.

No example of such a solution is known within the considered ansatz, apart from a possible example outside it, and important constraints have been obtained without proving the conjecture. The conjecture is also not fully excluded in the corresponding four-dimensional ${\cal N}=4$ gauged supergravity framework.