Bunkbed Conjecture Debunked?

[fresh_42]

TL;DR Summary

A new paper claims (not peer-reviewed, yet) that the bunkbed conjecture has been debunked by an example of a graph with $7222$ vertices.

I have just read about a mathematical conjecture that has presumably been debunked, the bunkbed conjecture. The Wikipedia link hasn't been updated since I wrote this post. The preprint reads

We give an explicit counterexample to the bunkbed conjecture introduced by Kasteleyn in $1985.$ The counterexample is given by a planar graph on $7222$ vertices and is built on the recent work of Hollom $(2024).$

There is a YouTube video ($\approx 15$ min.) that explains the situation quite well.

Besides curiosity, there are some things I learned/have been reminded of again that might be worth a discussion.

• There is a subject such as probabilistic combinatorics.
• I have never heard of the bunkbed conjecture before.
• $10^{-47}$ is enough to disprove an inequality.
• Neural networks become more and more important in modern mathematics.
• Neural networks do have their limits when their error margins are greater than the results.

The author of the video says that there have been numerous attempts to prove the conjecture, and now it seems that it cannot be proven. I hope that doesn't happen to the Riemann Hypothesis or the NP=P question.