The cactus-rank conjecture for generic cubic forms

Let $F\in k[x_0,\ldots,x_n]$ be a generic homogeneous cubic form, and let $cr(F)$ denote its cactus rank and $r(F)$ its rank. Cactus-rank conjecture. The cactus rank equals the rank when $n\leq 7$, and

$$cr(F)=2n+2$$

when $n\geq 8$. The preceding theorem gives the upper bound $cr(F)\leq 2n+2$; the conjecture specifies the exact generic cactus rank in all dimensions, with the first potentially strict case at $n=8$.