Parisi's random assignment conjecture

For a complete bipartite graph $K_{n,n}$ with independent exponentially distributed edge appearance times of rate $1$, let $L_{nn}(n)$ denote the length of a minimum $n$-assignment, that is, a perfect matching, and let ${\rm E}(L_{nn}(n))$ be its expected length. Parisi's conjecture.

$${\rm E}(L_{nn}(n))=1+\frac{1}{4}+\frac{1}{9}+\dots+\frac{1}{n^2}.$$

Proposed by Parisi in 1998, this conjecture had been verified up to $n=7$ at the time of the source; it was subsequently proved by Aldous, so the finite-$n$ expectation is exactly the stated sum.