It is simple enough for an adversarial system to subvert some members via collusion and others via obstruction. Take something like Consul which can elect new members and remove old ones (often necessary in modern cloud architectures). What does 50.1% mean when the divisor can be changed?

And meshes are extremely weird because the whole point is to connect nodes that cannot mutually see each other. It is quite difficult to know for sure if you’re hallucinating the existence of a node two hops away from yourself. You’ve never seen each other, except maybe when the weather was just right one day months ago.

It does a decent job of conveying the essential idea for a broader readership: perturb a graph through its adjacency matrix just enough to make the universality conjecture hold for the distribution of eigenvalues -> analytically establish that the perturbation was so small that the result would carry back to the original adjacency matrix (I imagine this is an analytical estimate bounding the distance between distributions in terms of the perturbation) -> use the determined distribution to study the probability of the second eigenvalue being concentrated around the Alon-Bopanna number.

I haven't had a chance to read the paper and don't work in graph theory but close enough to have enjoyed the article.

Unless you are a research scientist at an AI research company or top hedge fund, the interviewer should be best prepared to answer why they really need someone to know these proofs in their actual job.

Haven't read the paper, but wonder if this is the same ln(2) that comes up as the constant in rate monotonic scheduling.