  We study the liberation process for projections: $(p,q)\mapsto (p_t,q)=
(u_tpu_t^\ast,q)$ where $u_t$ is a free unitary Brownian motion freely
independent from $\{p,q\}$. Its action on the operator-valued angle $qp_tq$
between the projections induces a flow on the corresponding spectral measures
$\mu_t$; we prove that the Cauchy transform of the measure satisfies a
holomorphic PDE. We develop a theory of subordination for the boundary values
of this PDE, and use it to show that the spectral measure $\mu_t$ possesses a
piecewise analytic density for any $t>0$ and any initial projections of trace
$\frac12$. We us this to prove the Unification Conjecture for free entropy and
information in this trace $\frac12$ setting.
