4 problems

Bounded-support conjecture. The support $\operatorname{Supp}(f)$ must be a finite set.

Let the support of a $p$-adic Hahn expansion be the ordered set of exponents with nonzero coefficients, and let its order type be the order type of that set. Kedlaya's prediction.…

Let a $p$-adic algebraic number be represented as a $p$-adic Hahn series, and call its support bounded when it is bounded in the relevant ordered exponent group. Bounded-support fi…

Let $\alpha$ and $\beta$ be irrational and multiplicatively independent. Let $F(x)$ be a Hahn series over $\mathbb{R}$ that is both $\alpha$-Mahler and $\beta$-Mahler. Irrational M…