An Improved Example for an Autoconvolution Inequality

We give a nonnegative step function with 575 equally spaced intervals such that ‖f∗f‖L2(R)2‖f∗f‖L∞(R)‖f∗f‖L1(R)≥0.901564. This improves upon a recent result of Deepmind’s AlphaEvolve from May 2025, which found a nonnegative step function with 50 equally space intervals for which the left hand side is ≥0.8962. Our function was found using simulated annealing and gradient based methods.