Tachyon within the (ρ,τ,σ_I) sector

Prove that for any classical de Sitter solution of type II supergravity compactifications respecting the stated ansatz, a tachyonic direction always lies within the universal scalar sector spanned by the overall volume ρ, the four-dimensional dilaton τ, and the anisotropy moduli σ_I.

Background

This conjecture, originating in earlier work and summarized here, targets a minimal, universal subset of scalar fields and has been tested across many group-manifold de Sitter solutions without counterexamples on compact manifolds.

Although compelling, the review makes clear that a general proof has not been obtained, and the result may depend on compactness assumptions.