Classification of domains admitting an ultra-Euclidean function

Let $R$ be a Euclidean domain, and suppose that $R$ admits an ultra-Euclidean function. Ultra-Euclidean classification conjecture. Then either $R$ is a field or there is a field $\mathbb{K}$ such that

$$R\cong\mathbb{K}[x].$$

The source presents this as a consequence that would follow if the preceding preservation conjecture were true. The supplied status evidence marks the preceding conjecture as disproved, but gives no independent resolution of this conditional classification claim; its status should therefore be checked in the source.