Superpolynomial convergence in the Riemann Rearrangement Theorem

The paper establishes superpolynomial greedy approximation for Hausdorff moment sequences via a precise Main Lemma that requires entering a “close” regime (an ≤ x ≤ an+1) and then bootstraps across discrete-difference levels; this yields Theorems 1–2 with clear conditions and a countable exceptional set. The candidate solution mirrors the high-level structure (exceptional set via eventual alternation, two-step forcing, Δ-level bootstrapping), but its Pillar 1 contains a critical error: it asserts that whenever two consecutive greedy signs are equal, then min{|e_n|,|e_{n+1}|} ≤ Δx_n. That bound is not generally true unless one is already in the close regime. The paper instead proves Δ-closeness at specific indices via a more delicate pattern (−,+,+) argument, avoiding this gap. The candidate also understates the automatic tail condition (it holds eventually for any α>0, not only for α≤1). Thus, while the conclusions resemble the paper’s, the model’s proof has a substantive logical gap in its Main Lemma.