Linearizability conjecture for the Riccati chain

Let $F=F(x,y)$ and let $\Omega^n[y]$ denote the $n$-fold iterative equation in the Riccati chain. For $n\geq 3$, consider

$$\Omega^n[y]=0.$$

Linearizability conjecture. For $n\geq 3$, the equation is linearizable if and only if $F_y=0$; in that case, it is already a linear equation. The claim extends the verified analysis for the third- and fourth-order equations. It proposes that no higher iterate of a nonlinear equation in the chain becomes linearizable, an issue left open for $n>4$.