Derivative-free validity conjecture for the sink theorem

Let $f$ be a map in the setting of Theorem 1, and interpret “without any extra assumptions on the derivative” as removing the hypothesis that $Df$ is never the null map.

Derivative-free validity conjecture. The result of Theorem 1 remains valid without any extra assumptions on the derivative.

The authors describe the non-null-derivative assumption as a likely artifact of the proof; whether the theorem extends in this form is left open.