Submaximal-rank classification conjecture for multiplicity-one operator identities

Let $R$ be an operator identity of degree $3$ and multiplicity $1$ on an associative triple system. Let $v\in\mathbb{F}^4$ be the coefficient vector of $R$, and suppose that $v$ produces submaximal rank in the matrix of consequences, without restrictions on its components. Multiplicity-one classification conjecture. $R$ is equivalent to one of the identities of the stated multiplicity-one classification theorem. This conjecture asserts that the submaximal-rank classification remains valid without restricting the components of $v$ to $\{0,\pm1,\pm2\}$.