Topological Entropy of Diagonal Maps on Inverse Limit Spaces

The paper establishes Ent(Fn ∘ Fm^{-1}) = max{log n, log m} under Fn ∘ Fm^{-1} = Fm^{-1} ∘ Fn for open piecewise-monotone interval maps via sharp lower bounds (horseshoes) and a nontrivial combinatorial upper bound (Theorem 4.19), culminating in Theorem 4.20 . The candidate solution’s lower bounds are on the right track, but its upper bound appeals to a Dinh–Sibony “dynamical degree” principle that does not apply to these real one-dimensional set-valued correspondences; thus the model’s proof is incomplete/incorrect even though it reaches the correct final formula.