  The factorization theorem for exclusive processes in perturbative QCD
predicts the behavior of the pion electromagnetic form factor $F(t)$ at
asymptotic spacelike momenta $t(=-Q^2)<0$. We address the question of the onset
energy using a suitable mathematical framework of analytic continuation, which
uses as input the phase of the form factor below the first inelastic threshold,
known with great precision through the Fermi-Watson theorem from $\pi\pi$
elastic scattering, and the modulus measured from threshold up to 3 GeV by the
BaBar Collaboration. The method leads to almost model-independent upper and
lower bounds on the spacelike form factor. Further inclusion of the value of
the charge radius and the experimental value at $-2.45 \gev^2$ measured at JLab
considerably increases the strength of the bounds in the region $ Q^2 \lesssim
10 \gev^2$, excluding the onset of the asymptotic perturbative QCD regime for
$Q^2< 7\gev^2$. We also compare the bounds with available experimental data and
with several theoretical models proposed for the low and intermediate spacelike
region.
