Uniqueness conjecture for metric-affine torsion waves

Let $c_j$ be the weights in the metric-affine action, and let Minkowski space be equipped with connections of the form

$$\Gamma(x)=\Gamma'\cos(k\cdot x)+\Gamma”\sin(k\cdot x),\quad k\ne0,\quad R(x)\not\equiv0.$$

Here $R(x)$ denotes the curvature of the connection, and the torsion waves are the solutions constructed in Section. Torsion-wave uniqueness conjecture. For generic weights $c_j$, torsion waves are the only solutions of the metric-affine Euler–Lagrange problem among these connections in Minkowski space. The conjecture is motivated by the system being heavily overdetermined; special choices such as the Yang–Mills weights admit wider families, so the genericity qualification is essential.