  We investigate the properties and structure of the recently discussed "fully
inclusive jet correlator", namely, the gauge-invariant field correlator
characterizing the final state hadrons produced by a free quark as this
propagates in the vacuum. Working at the operator level, we connect this object
to the single-hadron fragmentation correlator of a quark, and exploit a novel
gauge invariant spectral decomposition technique to derive a complete set of
momentum sum rules for quark fragmentation functions up to twist-3 level; known
results are recovered, and new sum rules proposed. We then show how one can
explicitly connect quark hadronization and dynamical quark mass generation by
studying the inclusive jet's gauge-invariant mass term. This mass is, on the
one hand, theoretically related to the integrated chiral-odd spectral function
of the quark, and, on the other hand, is experimentally accessible through the
$E$ and $\tilde{E}$ twist-3 fragmentation function sum rules. Thus,
measurements of these fragmentation functions in deep inelastic processes
provide one with an experimental gateway into the dynamical generation of mass
in Quantum Chromodynamics.
