The Trichotomy Conjecture for untranscendable linear orders

Let $\varphi$ be an untranscendable linear order. A linear order is strongly indecomposable when [the source context does not provide a definition]. An uncountable real type is the order type of an uncountable subset of $\mathbb{R}$. The Trichotomy Conjecture. For every untranscendable linear order $\varphi$, at least one of the following holds: $\varphi$ is strongly indecomposable, $\varphi$ contains an uncountable real type, or $\varphi=2$. This conjecture asks whether uncountable real types, together with the exceptional type $2$, account for all untranscendable orders that are not strongly indecomposable; the source presents it as an open problem, possibly assuming $\mathsf{PFA}$ as indicated by its name.