After some experimentation using the tool AlphaEvolve, the author was led to conjecture a proof of (1.28) by separately lower bounding each of these two factors. The first of these conjectures was then proven by ChatGPT, and the author was able to prove the second, thus giving a complete proof of Theorem 1.4.
1. AI contributions to Erdős problems
2. Claude’s Cycles [pdf]
Claude’s Cycles (Cont.) (via Bo Wang on Twitter)
3. A Ramsey-style Problem on Hypergraphs (FrontierMath Open Problems: Moderately Interesting)
4. Part of a theorem in Terence Tao’s Local Bernstein theory, and lower bounds for Lebesgue constants (via Jared Duker Lichtman on Twitter)
generating an notification because I added a couple answers