Remark: Family 191. A power improvement in the Heilbronn triangle problem

For every sufficiently large $n$, constructs $n$ points in the unit square such that every triangle has area at least $n^{-2+c}$ for one absolute $c>0$. This disproves the conjectured almost-$n^{-2}$ upper bound in Heilbronn's triangle problem, which asks how large the smallest determined triangle can be.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.