Paper presents a claimed optimal-scale sample bound for real-valued uniform convergence

In a paper submitted to arXiv on Oct. 17, 2026, Noga Alon, Steve Hanneke, Shay Moran and Tom Waknine say they obtain error γ+ε using order d/ε² samples, where d is the fat-shattering dimension at scale γ. They say earlier results achieved either the optimal scale or the optimal sample bound, while their result achieves both. The paper also describes covering and chaining tools used in the work.