Uniqueness conjecture for Riemannian metric-affine solutions

Consider the metric-affine Euler–Lagrange problem for the action with weights $c_j$, restricted to Riemannian spacetimes, meaning spacetimes with metric-compatible connections. Thompson spaces and Einstein spaces are the two families of Riemannian solutions constructed in the paper. Riemannian uniqueness conjecture. For generic weights $c_j$, Thompson spaces and Einstein spaces are the only Riemannian solutions of the metric-affine Euler–Lagrange problem. The claim is a uniqueness assertion within the Riemannian class; the paper notes that the equations are heavily overdetermined and that special weights can produce additional solutions.