Disjoint Frequently Hypercyclic Pseudo-Shifts

The paper’s Disjoint A-Hypercyclicity Criterion (Theorem 2.1) is proved by a careful normalization/diagonal argument that yields a blockwise uniform tail control and a convergent global series x, followed by an error decomposition giving ||T_j^n x − y_{l,j}|| ≤ (l−1)ε_l + ∑_{k≥l} ε_k + ε_l → 0 uniformly over n ∈ A_l and j ∈ [N] (see the statement and proof around Theorem 2.1 and the subsequent construction of x, which explicitly implements the diagonal tail control and convergence of x) . By contrast, the model’s Step 1 incorrectly assumes a single M that simultaneously enforces tail bounds of size ε_l for all blocks l, which does not follow from “unconditional convergence uniformly in l”; the paper circumvents this with a subsequence/diagonalization normalization. Steps 2–3 of the model follow the same error decomposition as in the paper and are otherwise aligned.