The rational Robba-ring admissibility conjecture

Let $\mathcal R_{\mathbb Q}=\bigcup_N\mathcal R_{1/N}$ be the rational Robba ring over $\mathbb C_p$, completed under the Gauss norm. Rational Robba-ring admissibility conjecture. The completed rational Robba ring is an admissible decomposing Banach algebra in the sense of Birkhoff–Rott–Samelson, and consequently admits scalar and matrix Wiener–Birkhoff factorizations with rational partial indices. This is proposed as a non-archimedean analogue of the factorization theory developed for the adelic Wiener algebra; its status is not resolved in the supplied text.