Confirmation of the Daykin-Frankl Conjecture

In 1983, Daykin and Frankl conjectured that if $P$ is a convex subset of $Q_n$, then it contains at least $\mathrm{\mid }P\mathrm{\mid }\left(\genfrac{}{}{0px}{}{n}{\lfloor n\mathrm{/}2\rfloor }\right)2^{-n}$ pairwise incomparable elements. We verify and communicate an LLM-generated proof of this conjecture.