Eventual Square Pyramid Optimality for Five-Point Riesz Energy

We prove that, for every sufficiently large real exponent s, the unique five-point minimizer of chordal Riesz s-energy on the unit two-sphere, up to orthogonal congruence and relabeling, is a square pyramid. Its apex is the north pole and its base has latitude -t, where (1-t)^(s/2+1)=(2+2^(-s/2))*t. Starting from the limiting configuration theorem of Bondarenko, Hardin and Saff, we use angular stationarity and relative height balance to localize every minimizer within o(1/s) of this moving pyramid. A uniform positive Hessian in a surrounding coordinate box proves uniqueness. The threshold is existential: the argument does not identify the transition exponent or settle the intervening range of exponents. This is an unrefereed preprint; no absolute priority claim is made.