Lower bound $0.38055470$ for Erdős's minimum overlap constant

A rigorous lower bound $c > 0.38055470$, improving White's $0.379005$ (2022). The problem stays open: the best public upper bound is $0.3808585749$ (Einstein Arena, August 2026; $0.380868$ in the literature, SimpleTES), so $c$ is now known to within about $3 \times 10^{-4}$. The bound rests on a finite certificate checked in ball arithmetic plus a step-function transfer from the continuous to the finite problem. The later Station paper (arXiv 2608.23691) reaches $0.380552$, below this; a higher claim of $0.3805634$ posted to the tracker on 19 September is unchecked.

A rigorous lower bound $c > 0.38055470$, improving White's $0.379005$ (2022). The problem stays open: the best public upper bound is $0.3808585749$ (Einstein Arena, August 2026; $0.380868$ in the literature, SimpleTES), so $c$ is now known to within about $3 \times 10^{-4}$. The bound rests on a finite certificate checked in ball arithmetic plus a step-function transfer from the continuous to the finite problem. The later Station paper (arXiv 2608.23691) reaches $0.380552$, below this; a higher claim of $0.3805634$ posted to the tracker on 19 September is unchecked.