  We find an asymptotic solution for two-, three- and multi-point correlators
of local gauge-invariant operators, in a lower-spin sector of massless
large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that
the solution is asymptotic in the ultraviolet to renormalization-group improved
perturbation theory, by means of a new purely field-theoretical technique that
we call the asymptotically-free bootstrap, based on a recently-proved
asymptotic structure theorem for two-point correlators. The asymptotically-free
bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of
glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends
only on the unknown particle spectrum, but not on the anomalous dimensions, as
a consequence of the $LSZ$ reduction formulae. Very many physics consequences
follow, both practically and theoretically. In fact, the asymptotic solution
sets the strongest constraints on any actual solution of large-$N$ $QCD$, and
in particular on any string solution.
