Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 176-01. The second Kahn–Kalai conjecture
Manuscript map · lines 5655–5664
OpenAI@2026-10-07#rem:oai-p-176-01
Authors: OpenAI. Family 176.
Title: The second Kahn–Kalai conjecture.
Abstract: We prove the second Kahn–Kalai conjecture. For every finite simple graph H with h ≥ 1 edges and at most n vertices, the threshold for $G(n,p)$ to contain an ordinary copy of H is at most $C p_{{}mathrm E}(n,H)(1+{}log_2 h)$, where C is universal. Here $p_{{}mathrm E}(n,H)$ is the least density at which every subgraph of H has expected copy count at least one half.
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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