Coherence Structures and Monad Dynamics in Homotopy Type Theory within an (∞,1)-Topos

We study coherence structures in homotopy type theory interpreted in an (∞,1)-topos in the sense of Lurie. We introduce a monadic endofunctor on the ambient ∞-topos which models iterated identity formation and coherence refinement as internal categorical dynamics. Using homotopy cardinality, we define a notion of asymptotic growth under iteration of this monadic structure. All constructions are internal to the semantic interpretation of homotopy type theory in an ∞-topos with univalence. No additional axioms beyond standard homotopy type theory are introduced. The paper also discusses categorical structural constraints and conjectural asymptotic regimes of the induced dynamical system.