The minimal-degree uniqueness conjecture for quantizations of principal-orbit points

Let $\mathcal{O}_1$ be the principal orbit in $\mathbb{P}^2(\mathbb{Q})$, and let $\mathcal{Q}(p)$ be the set of quantizations of $p\in\mathcal{O}_1$ in $\mathbb{P}^2(\overline{\Lambda})$. A deformation is a point $[R:S:T]\in\mathcal{Q}(p)$, represented by polynomials in $q$. The minimal-degree uniqueness conjecture. For every $p\in\mathcal{O}_1$, there is a unique deformation $[R:S:T]$ in $\mathcal{Q}(p)$ such that $\deg(R)$, $\deg(S)$ and $\deg(T)$ are minimal. The preceding examples motivate the search for a canonical representative of each quantized point, while uniqueness is not established in the source.