Five Point Energy Minimization: A Synopsis

This paper is a condensation of my arXiv monograph entitled Schwartz "The phase transition in 5 point energy minimization", 2016. arXiv:1610.03303, which contains a complete proof that there is a constant 15.0488 such that the triangular bi-pyramid is the minimizer, amongst all 5 point configurations on the sphere, with respect to the power law potential Rs (r) = sign(s)/r s, if and only if s. (-2, 0). (0,.]. In this paper we explain the main ideas and give proofs for some of the key lemmas.