  Future hadron colliders will have a remarkable capacity to discover massive
new particles, but their capabilities for precision measurements of couplings
that can reveal underlying mechanisms have received less study. In this work we
study the capability of future hadron colliders to shed light on a precise,
focused question: is the higgs mass of 125 GeV explained by the MSSM? If
supersymmetry is realized near the TeV scale, a future hadron collider could
produce huge numbers of gluinos and electroweakinos. We explore whether
precision measurements of their properties could allow inference of the scalar
masses and $\tan \beta$ with sufficient accuracy to test whether physics beyond
the MSSM is needed to explain the higgs mass. We also discuss dark matter
direct detection and precision higgs physics as complementary probes of $\tan
\beta$. For concreteness, we focus on the mini-split regime of MSSM parameter
space at a 100 TeV $pp$ collider, with scalar masses ranging from 10s to about
1000 TeV.
