Breakthrough Tracker record
The bunkbed conjecture is false
The authors construct an explicit finite planar graph with 7,222 vertices that violates the bunkbed percolation inequality.
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- Stable ID
math-bunkbed-conjecture-disproof-2025- Revision
math-bunkbed-conjecture-disproof-2025.v1- Field
- Mathematics · Probability and graph theory
- Evidence
- Tier 1 · Peer reviewed: Yes
- Record state
- Current · Peer-reviewed published disproof
- Last checked
AI role
No generative-AI role was disclosed; computation and search aided discovery, while the final proof is mathematical.
Record details
- Problem or result
- Bunkbed conjecture in percolation
- Authors
- Nikita Gladkov, Igor Pak and Aleksandr Zimin
- Institutions
- University of California, Los Angeles and Massachusetts Institute of Technology at publication
- Result date
- Preprint October 3, 2024; published June 13, 2025
Why it matters
The peer-reviewed counterexample overturns an intuitively compelling conjecture studied for roughly four decades.
Limits
The disproof does not show that every bunkbed-type inequality fails. Restricted graph classes and related variants may remain true.
Sources
- Primary: Gladkov, Pak and Zimin, The bunkbed conjecture is false
- Primary: Peer-reviewed PNAS article
- Independent: Quanta, Math's 'Bunkbed Conjecture' Has Been Debunked
Correction and revision history
- Added on 2026-07-22 as the only peer-reviewed published disproof in the initial 16-card mathematics set.
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