Remark: Family 176. The second Kahn–Kalai conjecture

Proves the second Kahn–Kalai conjecture: for every finite simple graph $H$ with $h\ge 1$ edges and at most $n$ vertices, its appearance threshold in $G(n,p)$ is at most $C{p}_{\mathrm{E}}(n,H)(1+{\log }_{2}h)$, with universal $C$. Here $p_{\mathrm{E}}$ is the least density at which every subgraph of $H$ has expected copy count at least $1/2$.

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.