  This work has been expanded and fully incorporated into arXiv:1203.5837.
  Cases of equality in the classical 2-negative type inequalities for Hilbert
spaces are characterized in terms of balanced signed simplices. It follows that
a metric subspace of a Hilbert space H has strict 2-negative type if and only
if it is affinely independent (when H is considered as a real vector space).
This allows a complete description of Shkarin's class M.
