The functor-of-points conjecture for $cwidehat{\bbF}_1^\mathrm{Syn}$

Let $\bbS^{\widehat{\mathbbl{\Delta}}}$ be the complement of the zero section in the universal formal group $\widehat{\bbG}_\mathrm{univ}=\bbS^{\widehat{\calN}}$, regarded as an analytic stack. For a $p$-nilpotent ring $R$, let $\widehat{\bbF}_1^\mathrm{Syn}$ be the stack cited in the source. Functor-of-points conjecture. An $R$-point of $\widehat{\bbF}_1^\mathrm{Syn}$ is given by a formal group over $R$ together with a $p$-complete strict ring structure on the pullback of $\bbM_{\mathrm{m}\ifthenelse{\equal{\bbS}{}}{}{,\bbS}}^{\widehat{\calN}}$ to

$$\operatorname{Spec}R\times_{\calM_\mathrm{fg}}\bbS^{\widehat{\mathbbl{\Delta}}}.$$

This gives a proposed moduli description of $\widehat{\bbF}_1^\mathrm{Syn}$ in terms of formal groups and strict ring structures.