  Analyses of the pion valence-quark distribution function (DF),
${u}^\pi(x;\zeta)$, which explicitly incorporate the behaviour of the pion wave
function prescribed by quantum chromodynamics (QCD), predict ${u}^\pi(x\simeq
1;\zeta) \sim (1-x)^{\beta(\zeta)}$, $\beta(\zeta \gtrsim m_p)>2$, where $m_p$
is the proton mass. Nevertheless, more than forty years after the first
experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of
${u}^\pi$, the empirical status remains uncertain because some methods used to
fit existing data return a result for ${u}^\pi$ that violates this constraint.
Such disagreement entails one of the following conclusions: the analysis
concerned is incomplete; not all data being considered are a true expression of
qualities intrinsic to the pion; or QCD, as it is currently understood, is not
the theory of strong interactions. New, precise data are necessary before a
final conclusion is possible. In developing these positions, we exploit a
single proposition, viz. there is an effective charge which defines an
evolution scheme for parton DFs that is all-orders exact. This proposition has
numerous corollaries, which can be used to test the character of any DF,
whether fitted or calculated.
