Injectivity conjecture for the ultradiscretized mapping

Let $X\in\mathbb{R}^{M\times N}$ and let $\mathrm{UD}(\eta)$ denote the ultradiscretization of the mapping $\eta$ constructed from the divisor component and the ultradiscretized mapping $i$. Injectivity conjecture. The mapping $\mathrm{UD}(\eta)$ is injective. This is proposed by analogy with the corresponding discrete result; the source provides no resolution, so the conjecture remains open.