The conjecture that random generalized power series are irreducible

Let $K$ be a field and let $b\in K((\mathbb{R}^{\leq 0}))$ be a random generalized power series, meaning that either $\operatorname{cl}(\operatorname{supp}(b))-\{0\}$ is $\mathbb{Q}$-linearly independent or the tuple of coefficients indexed by $\operatorname{supp}(b)$ is algebraically independent over $\mathbb{Q}$. Let $\sup(b)$ be the supremum of the support, $\operatorname{ot}(b)$ its order type, and define $\deg(b)$ as the maximum ordinal $\alpha$ such that $\omega^\alpha\leq\operatorname{ot}(b)$. Random-series irreducibility conjecture. If $\sup(b)=0$, then $b$ is irreducible, and so is $b+r$ for every series $r$ satisfying

$$\operatorname{ot}(r)<\omega^{\deg(b)}.$$

The paper proves this assertion for substantial families of order types and notes that the conjecture would extend those results to all random series; its general status is not specified.