The Pełczyński decomposition conjecture for commutators

Let $\mathcal{X}$ be a Banach space such that

$$\mathcal{X}\simeq \big (\sum \mathcal{X}\big )_p,$$

where $1\leq p\leq\infty$ or $p=0$ (we say that such a space admits a Pełczyński decomposition). Assume that $\mathcal{L}(\mathcal{X})$ has a largest ideal $\mathcal{M}$. Commutator classification conjecture. Every non-commutator on $\mathcal{X}$ has the form $\lambda I+K$, where $K\in\mathcal{M}$ and $\lambda\neq 0$. This conjecture is suggested by the known classifications of commutators on $\ell_p$ for $1\leq p\leq\infty$ and on $c_0$, but its validity for general Banach spaces satisfying the stated decomposition and ideal hypotheses remains open.