Fagundes–Mello conjecture on images of multilinear polynomials on upper triangular matrix algebras

Let $K$ be a field, let $n\geq 2$ be an integer, and let $p$ be a multilinear polynomial in noncommuting variables. Let $T_n(K)$ denote the algebra of all $n\times n$ upper triangular matrices over $K$. Fagundes–Mello conjecture. The image of $p$ on $T_n(K)$ is always a vector space. This is a variation of the Lvov–Kaplansky image problem for upper triangular matrix algebras. The supplied text does not state whether the conjecture has been resolved.