The reviewers point out that this is a borderline submission. They reasonably questions several things in the paper: - it is not clear why the coefficients for which the CLT holds for are important; - assumptions are restrictive; - the paper studies too simplistic of a model; - parts of the analysis are unclear; - writing is done hastily with typos lingering around. After my own reading, I agree with these comments. On the other hand, the reviewers also point out that there are certain aspects of double descent that are not previously explored, which are of more interest compared to the confidence intervals. My opinion is that the paper would be much stronger if the cons were addressed in a revised manuscript.