Square Entropy and Uniform n-to-1 Bernoulli Transformations

The paper’s classification theorem (Theorem 4.5) asserts that uniform n-to-1 (m,l)-Bernoulli transformations are isomorphic iff they share the same square entropy, but its proof jumps from equality of square entropies to isomorphism without establishing that all uniform n-to-1 full zip shifts with the same (m,l) (equivalently same (m,n) with l = mn) are mod-0 conjugate; that canonical conjugacy is not proved in the paper. The candidate solution correctly computes the forward/backward entropies, uses the fixed-n constraint to recover (log m, log l) from h_S, and crucially supplies an explicit canonical conjugacy S ≅ Z×[n], filling the missing step. The paper also contains a plus/minus mismatch in Lemma 2.6 but this does not affect h_S; it does, however, signal that notation needs correction.