Concavity conjecture for the fundamental ratio on triangle moduli space

Let $\xi(D)=\lambda_2(D)/\lambda_1(D)$ be the fundamental ratio of the first two Dirichlet–Laplacian eigenvalues. Consider the moduli space of triangles after quotienting by the symmetries of the problem. Concavity conjecture for the fundamental ratio. The function $\xi$ is concave on this moduli space.

This claim is suggested by numerical and visual evidence from the paper's parameter-space computations; no proof or resolution is supplied.