Algebraic specification conjecture for quasi-admissibility in the Belgian Chocolate Problem

Let $x$ and $y$ be polynomials of degree at most $n$, and let $[?]$ denote the supremum of the optimization problem in the Belgian Chocolate Problem. A value of $[?]$ is quasi-admissible if it can be achieved by polynomials $x,y,z$ formed via algebraic specification.

Algebraic specification conjecture. For all $n$, $[?]$ is quasi-admissible by some $x,y,z$ that are formed via algebraic specification.

The conjecture formalizes the empirical observation that admissible values approach quasi-admissible values obtained through algebraic specification. The source provides numerical evidence and notes that $[?]$ is not admissible by $x,y$ of degree at most $n$, but does not establish the conjecture.