Classification conjecture for algebras of Jordan type

Let $A$ be a commutative non-associative algebra over a field of characteristic not $2$, generated by primitive axes and satisfying the fusion law of Jordan type $\eta$. A factor of a Matsuo algebra means a non-zero quotient of a Matsuo algebra, which remains an algebra of Jordan type.

Classification conjecture. Every algebra of Jordan type is either a Jordan algebra, a Matsuo algebra, or a factor of a Matsuo algebra.

This conjecture asserts that Jordan algebras, Matsuo algebras, and their non-zero factors exhaust the known class of algebras of Jordan type. It remains open, although some cases have been completed.