From a very quick glance at page 6 of https://arxiv.org/pdf/2310.05328.pdf https://arxiv.org/pdf/2310.05328.pdf You can see he is treating the case of k=1,2 wi

From a very quick glance at page 6 of https://arxiv.org/pdf/2310.05328.pdf https://arxiv.org/pdf/2310.05328.pdf You can see he is treating the case of k=1,2 with that formula and uses induction to extend it to 1 ≤ 𝑘 ≤ 𝑛 − 2. For k = n - 1 he uses a different bound defined in equation 2.2. So he bypasses the issue.