Strong Martio's conjecture for quasiregular mappings

Let $U \subset \mathbb R^n$ be open with $n \ge 3$, let $f:U\to f(U)\subset\mathbb R^n$ be a non-constant quasiregular mapping, let $K_I(f)$ denote its inner dilatation, and let $\mathcal{B}_f$ be its branch set. For $x\in U$, write $i(x,f)$ for the local topological index of $x$ under $f$. Strong Martio's conjecture. The inner dilatation satisfies

$$\inf_{x\in\mathcal{B}_f} i(x,f)\le K_I(f).$$

This is a generalization of Martio's conjecture, which asserts that a non-constant quasiregular mapping with $K_I(f)<2$ is a local homeomorphism. The conjecture is presented as a long-standing unconfirmed problem; the source gives no resolution of the stronger inequality.