Positive-definite structured-tensor conjecture for uniqueness of nonlinear complementarity solutions

Let $m$ and $n$ be positive integers, let $\boldsymbol{q}in\boldsymbol{R}^{n}$, and let $\mathcal{A}in ST_{m,n}$ be a structured tensor. The tensor $\mathcal{A}$ is positive definite when it satisfies the positive-definiteness condition used for $ST_{m,n}$, and $NCP(\mathbf{q},\mathcal{A})$ denotes the nonlinear complementarity problem associated with $\mathbf{q}$ and $\mathcal{A}$. The positive-definite structured-tensor conjecture. If $\mathcal{A}in ST_{m,n}$ is positive definite, then $NCP(\mathbf{q},\mathcal{A})$ has a unique solution. This conjecture asks whether the diagonalizability assumption in part (a) of Theorem 5 can be removed; resolving it would establish uniqueness under positive definiteness alone.