  The vector and axial-vector ALEPH hadronic spectral functions from
$\tau$-decay are used to probe potential quark-hadron duality violations (DV).
This is done in the framework of finite energy QCD sum rules (FESR). A pinched
integration kernel is introduced in the FESR in order to (a) quench potential
duality violations on the real axis in the complex squared energy $s$-plane,
and (b) effectively extend the analysis well beyond the kinematical
$\tau$-decay end-point where there is no longer data, i.e.\ in the range $s = 3
- 10 \,{\mbox{GeV}}^2$. In the vector channel this procedure is supplemented
with actual data from $e^+ e^-$-annihilation into hadrons, above the tau-decay
kinematical end-point, with results fully supporting this extension. Very good
agreement is obtained between data and two specific pinched FESR. Results from
this analysis are confronted with those from a specific model of DV. As the sum
rules are well satisfied in both cases within experimental errors, we conclude
that possible DV must be buried under the experimental uncertainties. In other
words, there seems to be no need for explicit models of DV in this case.
Pinched kernels work as well, but with far less free parameters.
