Minimality conjecture for trace reductions of three 3x3 matrices

Let $R$ be an evaluation map obtained from the trace reduction referred to in the source, and let the chosen monomials be the monomials used to construct the corresponding generating set of trace relations. Minimality conjecture. If we choose $R$ as in the trace reduction, then the chosen monomials always form a minimal generating set. This asserts that the trace-reduction procedure produces a minimal generating set for the relevant kernel of the evaluation map; the supplied text gives no evidence that the conjecture has been resolved.