The symmetric rank conjecture for the skew matrix multiplication polynomial of size three

Let $sM_{\langle 3\rangle}$ denote the skew matrix multiplication polynomial of size $3$, and let ${\bold R}_s$ denote its symmetric rank, namely the least number of cubes of linear forms whose sum equals the polynomial. Numerical computations give a decomposition with $18$ summands. Symmetric rank conjecture.

$${\bold R}_s(sM_{\langle 3\rangle})=18.$$

The preceding lower and upper bounds are $14\leq {\bold R}_s(sM_{\langle 3\rangle})\leq18$, so the conjecture asserts that the numerically found decomposition is optimal. The decomposition was found numerically using Bertini, with all $18$ summands having rank $3$; an exact proof of the equality is not supplied here.