Formulate a dynamic (time-indexed) OHTT

Develop a dynamic formulation of Open Horn Type Theory with time-indexed contexts Γ_t, rules for the temporal evolution of coherence and gap judgments, a formal notion of persistent horns, and a scheduler or strategy that governs when to witness coherence versus gap, thereby extending the static calculus to a theory of judgmental dynamics.

Background

The static OHTT calculus treats coherence, gap, and open states timelessly, but many motivating phenomena (e.g., semantic drift) evolve over time.

The authors sketch components of a dynamic theory—time-indexed contexts, persistence, and a scheduler for witnessing decisions—and then declare that this dynamic development is not part of the current calculus.