Furter's two-polynomial Rigidity Conjecture

Let $m,n\in\mathbb N_+$ and let $a(X),b(X)\in{\mathbb C}[X]$ satisfy

$$a(X)\equiv b(X)\equiv X\pmod{X^2},\qquad \operatorname{deg}(a)\le m+1,\qquad \operatorname{deg}(b)\le n+1.$$

Rigidity Conjecture. If $a\circ b(X)\equiv X\pmod{X^{m+n+2}}$, then $a(X)=b(X)=X$. The paper introduces this conjecture after recording partial results on the length $2$ polydegree problem. Its general status is not resolved in the supplied text.