The dimension bound for four-generated primitive-axis Jordan-type algebras

Let $A$ be a $\mathcal{J}(\alpha,\beta)$-algebra generated by four primitive axes. Here, $\mathcal{J}(\alpha,\beta)$ denotes the class of algebras under consideration with eigenvalues governed by the parameters $\alpha$ and $\beta$, and an axis is called primitive when its $1$-eigenspace is one-dimensional. Dimension-bound conjecture. The dimension of $A$ satisfies

$$\dim(A)\leq 81.$$

The claim is motivated by rewriting rules for four-generated algebras of Jordan type and by a method that constructs multiplication tables from a basis of axes. Its status is not resolved in the supplied source context.