Universality conjecture for stratified critical-circle conjugacies

Let $g$, $h$, and $h^{-1}$ be the conjugacies associated with a critical invariant circle, and let $\kappa(\cdot)$ denote their regularity. A numerical characteristic is universal when it takes the same value on an open set of functions. Stratified conjugacy-regularity universality conjecture. The regularities $\kappa(g)$, $\kappa(h)$, and $\kappa(h^{-1})$ are universal numbers. This is a renormalization-group prediction about regularity characteristics of critical invariant circles; the source supplies no resolution and leaves the precise universality domains and function spaces implicit.