  The vanishing of the Higgs quartic coupling of the Standard Model at high
energies may be explained by spontaneous breaking of Higgs Parity. Taking Higgs
Parity to originate from the Left-Right symmetry of the $SO(10)$ gauge group,
leads to a new scheme for precision gauge coupling unification that is
consistent with proton decay. We compute the relevant running of couplings and
threshold corrections to allow a precise correlation among Standard Model
parameters. The scheme has a built-in solution for obtaining a realistic value
for $m_b/m_\tau$, which further improves the precision from gauge coupling
unification, allowing the QCD coupling constant to be predicted to the level of
1 % or, alternatively, the top quark mass to 0.2 %. Future measurements of
these parameters may significantly constrain the detailed structure of the
theory. We also study an $SO(10)$ embedding of quark and lepton masses, showing
how large neutrino mixing is compatible with small quark mixing, and predict a
normal neutrino mass hierarchy. The strong CP problem may be explained by
combining Higgs Parity with space-time parity.
