This paper has lead to a long and thoughtful discussion between the reviewers. The main points that were raised are the following: + The results are novel and close a long-standing gap between upper and lower bounds in a very important problem. - The presentation is subpar in that even a very well-versed expert of the topic had trouble verifying not only the proof details, but also the high-level intuition of the analysis. While the reviewers have agreed that the results are significant and they definitely bring the field forward, an expert reviewer argued that the step forward is perhaps not significantly big enough to warrant publication in the present form. However, after much discussion, the other reviewers made a strong case for acceptance and all reviewers agreed that the community would clearly benefit from this paper being published. That said, I strongly encourage the authors to work hard on improving the presentation for the final version.