  In this paper we compute the celestial operator product expansion between two
outgoing positive helicity gravitons in the self dual gravity. It has been
shown that the self dual gravity is a $ w_{1+\infty} $-invariant theory whose
scattering amplitudes are one loop exact with all positive helicity gravitons.
Celestial $w_{1+\infty}$ symmetry is generated by an infinite tower of
(conformally soft) gravitons which are holomorphic conserved currents. We find
that at any given order only a \textit{finite} number of $w_{1+\infty}$
descendants contribute to the OPE. This is somewhat surprising because the
spectrum of conformal dimensions in celestial CFT is not bounded from below.
However, this is consistent with our earlier analysis based on the
representation theory of $w_{1+\infty}$. The phenomenon of truncation suggests
that in some (unknown) formulation the spectrum of conformal dimensions in the
dual two dimensional theory can be bounded from below.
