Breaking the high-degree barrier in Lehmer's problem with a human-AI discovery loop

[arXiv] Yuri Chervonyi, Sergei Gukov, and Thang Luong propose a human-machine collaborative discovery loop that combines a numerical pipeline, symbolic verification, and large-scale distributed search to tackle the construction challenge of the 1933 Lehmer problem for high even-degree polynomials. The authors state that previous systematic constructions were mostly limited to even degrees d≤180, and that the Boyd family often skips nearly half of the target degrees due to factorization. The paper states that its five-parameter "generalized Boyd algorithm" eliminates degree skipping and constructs, for every target degree, irreducible integer-coefficient polynomials whose Mahler measure is strictly below the Boyd limit point α1≈1.255434; in evaluations for even degrees up to 2000, it improves six published best values and accounts for 99.6% of the known best records.