  It is popular to probe the structure of the QCD vacuum indirectly by studying
individual fermion eigenmodes, because this provides a natural way to filter
out UV fluctuations. The double-peaking in the distribution of the local chiral
orientation parameter (X) has been offered as evidence, by some, in support of
a particular model of the vacuum. Here we caution that the X-distribution
peaking varies significantly with various versions of the definition of X.
Furthermore, each distribution varies little from that resulting from a random
reshuffling of the left-handed (and independently the right-handed) fields,
which destroys any QCD-induced left-right correlation; that is, the
double-peaking is mostly a phase-space effect. We propose a new universal
definition of the X parameter whose distribution is uniform for randomly
reshuffled fields. Any deviations from uniformity for actual data can then be
directly attributable to QCD-induced dynamics. We find that the familiar double
peak disappears.
