Coherence Growth in Homotopy Type Theory via Monadic Dynamics in an (infinity,1)-Topos

We study iterated identity structures in homotopy type theory interpreted in an (∞,1)-topos in the sense of Lurie. We introduce a monadic endofunctor on the ambient ∞-topos that models coherence refinement and iterated identity formation as a dynamical system internal to the type-theoretic semantics. Using homotopy cardinality, we define a notion of asymptotic coherence growth under iteration. We analyze the resulting growth behavior as a conjectural dynamical phenomenon within the internal language of the ∞-topos. All constructions are compatible with standard homotopy type theory with univalence. No new logical axioms are introduced.