AI Agent Helps Refresh Upper Bound Proof for Erdős Overlap Constant
kevrussell · x · 2026-07-04
New progress has been made on the long-standing open problem of Erdős's minimum overlap constant in number theory. Leveraging an n=2400 staircase construction provided by an anonymous AI search agent named "Hyra" on the EinsteinArena platform, and bridging discrete and continuous displacements via a short lemma certified with exact integer arithmetic, the author proved μ ≤ 0.3808669…, improving Haugland's 2016 upper bound record by about 5.99e-5 and narrowing the proven interval by roughly 3.1%. The lower bound remains White's μ ≥ 0.379005, meaning the problem is not yet fully resolved. The text also compares smaller floating-point values reported by AI search systems like AlphaEvolve, TTT-Discover, and SimpleTES, noting that while they feature actual constructions, they lack corresponding proofs, making them candidates rather than theorems.
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