Nonattainment of the three-marginal Coulomb Monge problem
What the paper claims, in its own words
An optimal three-particle Coulomb configuration need not be a deterministic function of the first particle, even for smooth identical spatial densities. The Monge and Kantorovich infima agree, but the Monge infimum is not attained. The same phenomenon occurs for every inverse-power Riesz exponent in each dimension at least two, with a suitable density in each case.
The plain-language explainer for this entry is still coming.