Invariant field conjecture for substitutions in the Robba ring

Let $K$ be the coefficient field, let $\mathcal{R}$ be the Robba ring, and let $\varphi$ be a general overconvergent substitution. The fraction field $\operatorname{Frac}\mathcal{R}$ carries the induced substitution action.

Invariant field conjecture. In general,

$$(\operatorname{Frac}\mathcal{R})^{\varphi=1}=K.$$

This is the same invariant-field claim as the paper's overconvergent-substitution conjecture, stated later in informal form. It is therefore merged with that fuller formulation rather than recorded as a separate row.