Veit Elser kindly noted errors in:

On the other hand, we've already seen examples S(ka,kb,kc) < S(a,b,c) in the

The correct statement: We've seen an example S(ka,kb,kc,kd) > S(a,b,c,d), namely Michael Reid's example 1/3 = S(4k,5k,6k,7k) > S(4,5,6,7) for k > 1.