Exact value of the peak autoconvolution constant

Determine the exact value of \(C_{6.2}=\inf_f\|f*f\|_\infty\) for nonnegative probability densities supported on \([-1/4,1/4]\).

Background

The peak autoconvolution problem asks how small the maximum of the self-convolution of a compactly supported probability density can be. Its exact value is connected to the asymptotic size of generalized Sidon sets.

The paper reports existing lower and upper bounds and notes that the Station’s upper bound is weaker than the current frontier; no exact value is established.

References

Determining $C_{6.2}$ is connected to the asymptotic size of generalized Sidon sets, and its exact value remains unknown.

— Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment  (2608.23691 - Chung et al., 24 Aug 2026) in Section 3, subsection “Peak autoconvolution”