The explicit ghost conjecture for $U_5$

For $a=0,\dots,3$, define the ghost series

$$G^{(a)}(w,t)=1+\sum_{n=1}^{\infty}g_n^{(a)}(w)t^n\in\mathbb{Z}_5[w][[t]],$$

where

$$g_n^{(a)}(w)=\prod_{\substack{l\geq 2\l\equiv a\bmod 4}}(w-w_l)^{m_n^{(a)}(l)}$$

with the exponents $m_n^{(a)}(l)$ prescribed by the source. Set

$$w_k=\exp(5(k-2))-1$$

and let $\operatorname{Char}(U_5,w,a)\in\mathbb{Z}_5[[w]][[t]]$ satisfy

$$\operatorname{Char}(U_5,w_k,a)=\operatorname{Char}(U_5,k,a)$$

for every weight $k$. The explicit ghost conjecture. For every weight $k$ congruent to $a$ modulo $4$, $\operatorname{Char}(U_5,w_k,a)$ and $G^{(a)}(w_k,t)$ have the same Newton polygon. This conjecture asserts that the explicitly constructed ghost series reproduces the Newton polygons governing the $U_5$ slopes; the source does not state a resolution.