Heilbronn triangle

The quantity is the saving $\eta$ in $\Delta(n)\ge cn^{-2+\eta}$. A higher saving is better. The baseline is $\eta=2/(45435k+16)$, where $k=T^2+1$ and $T=\binom{\binom{163}{41}}{3}$; the displayed approximation comes from the follow-up. The claim assumes the manuscript’s determinant/carry, conditional-digit distribution, orbit, deletion and interpolation estimates. Lean covers finite packing and selected scales only.

OpenAI baseline: $\approx3.18\cdot10^{-236}$, released Oct 6, 2:58 PM PT.

These results are Claimed: their authors published them, and we have not checked them.