External-univalence conjecture for contextual models of SOGATs

Let $a54$ be a SOGAT, and let $a54$ be equipped with weakly stable identity types satisfying function extensionality and saturation, which is the condition called external univalence. Let $a54$ be the category of contextual models of $a54$, equipped with the previously defined classes of cofibrations, weak equivalences and fibrations. External-univalence conjecture. A SOGAT $a54$ satisfies external univalence if and only if the category $a54$ is a left-semi model category. The conjecture identifies external univalence with the model-categorical structure of contextual models and is intended to characterize when the homotopy-theoretic semantics behaves well.