  We consider the energy-critical (corotational) 1-equivariant wave maps into
the two-sphere. By the seminal work [53] of Rapha\"el and Rodnianski, there is
an open set of initial data whose forward-in-time development blows up in
finite time with the blow-up rate
$\lambda(t)=(T-t)e^{-\sqrt{|\log(T-t)|}+O(1)}$. In this paper, we show that
this $e^{O(1)}$-factor in fact converges to the universal constant $2e^{-1}$,
and hence these solutions contract at the universal rate
$\lambda(t)=2e^{-1}(T-t)e^{-\sqrt{|\log(T-t)|}}(1+o_{t\to T}(1))$. Our proof is
inspired by recent works on type-II blow-up dynamics for parabolic equations.
The key improvement is in the construction of an explicit invariant subspace
decomposition for the linearized operator perturbed by the scaling generator in
the dispersive case, from which we obtain a more precise ODE system determining
$\lambda(t)$.
