Suppose we want to minimize a polynomial p(x) = p(x1, . . . , xn), subject to some polynomial constraints q1(x), . . . , qm(x) ≥ 0, using the Sum-of-Squares (SOS) SDP hierarachy. Assume we are in the “explicitly bounded” (“Archimedean”) case where the constraints include xi ≤ 1 for all 1 ≤ i ≤ n. It is often stated that the degree-d version of the SOS hierarchy can be solved, to high accuracy, ...