Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 191-01. A power improvement in the Heilbronn triangle lower bound
Manuscript map · lines 5845–5854
OpenAI@2026-10-07#rem:oai-p-191-01
Authors: OpenAI. Family 191.
Title: A power improvement in the Heilbronn triangle lower bound.
Abstract: There are absolute constants ${}eta,c_1{}gt 0$ such that, for every sufficiently large integer n, one can choose n points in the unit square so that every triangle they determine has area at least $c_1n{}{-2+{}eta}$. Thus the almost n−2 upper-bound formulation of Heilbronn's triangle problem is false. The exponent η is fixed but extremely small.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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