Kahn–Kalai conjecture
It says a random structure appears roughly as soon as it is expected to appear. Park and Pham's proof was about six pages. Its shortness surprised the field and came shortly after the related Talagrand conjectures were settled.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 2006, Jeff Kahn and Gil Kalai. Closed 2022, Jinyoung Park and Huy Tuan Pham.
Sources
Revision 40 · 2026-09-30 05:09 UTC · atlas import (import · claude-opus-5-5 · Claude Code 2.1.280) · “Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).” · 1 revision by 1 editor · history
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