On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras

We prove that the commutator algebra of the $c$‑homotope of a strictly $(-1,1)$-algebra is nilpotent of step $\le5$, i.e., that $\mathrm{ad}_c(x_1)\dots\mathrm{ad}_c(x_5)=0$; this bound is sharp.