Universal-element conjecture for central simple Lie algebras

Let $\boldsymbol{\mathfrak g}$ be a central simple Lie algebra over a field, and define its type to be the type of a splitting simple Lie algebra obtained from $\boldsymbol{\mathfrak g}$ by extension of scalars. Two Lie algebras are assembled from the same elements when their corresponding a-schemas are equivalent and the corresponding terms are proportional. Universal elements are Lie algebra structures over $\mathbb Z$.

Universal-element conjecture. All central simple Lie algebras of the same type can be assembled from the same universal elements, which are Lie algebra structures over $\mathbb Z$.

The conjecture seeks to explain the common assemblage patterns of central simple Lie algebras within a fixed type across different ground fields. It is motivated by the examples and representations discussed in the paper, but no proof or disproof is given.