  If supersymmetry is broken directly to the Standard Model at energies not
very far from the unified scale, the Higgs boson mass lies in the range 128-141
GeV. The end points of this range are tightly determined. Theories with the
Higgs boson dominantly in a single supermultiplet predict a mass at the upper
edge, (141 \pm 2) GeV, with the uncertainty dominated by the experimental
errors on the top quark mass and the QCD coupling. This edge prediction is
remarkably insensitive to the supersymmetry breaking scale and to
supersymmetric threshold corrections so that, in a wide class of theories, the
theoretical uncertainties are at the level of \pm 0.4 GeV. A reduction in the
uncertainties from the top quark mass and QCD coupling to the level of \pm 0.3
GeV may be possible at future colliders, increasing the accuracy of the
confrontation with theory from 1.4% to 0.4%. Verification of this prediction
would provide strong evidence for supersymmetry, broken at a very high scale of
~ 10^{14 \pm 2} GeV, and also for a Higgs boson that is elementary up to this
high scale, implying fine-tuning of the Higgs mass parameter by ~ 20-28 orders
of magnitude. Currently, the only known explanation for such fine-tuning is the
multiverse.
