Elegant Six-Page Proof Reveals the Emergence of Random Structure

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical objects called random graphs — seemed too strong, too all-encompassing, too bold to possibly be true. It felt more like wishful thinking than a reflection of mathematical truth. Even so…

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