  We argue that the pattern of the deviation from the Glauber approximation
prediction for the centrality dependence of the rate of forward jet production
observed in pA collisions at the LHC provides the first experimental evidence
that parton configurations in the projectile proton containing a parton with
large $x$ interact with a nuclear target with a significantly smaller than
average cross section and have smaller than average size. We implement the
effects of fluctuations of the interaction strength and, using the ATLAS
analysis of how hadron production at backward rapidities depends on the number
of wounded nucleons, make quantitative predictions for the centrality
dependence of the jet production rate as a function of the $x$-dependent
interaction strength $\sigma(x)$.
  We find that \sigma(x)\sim 0.6 ~\sigma_{tot}(pp) gives a good description of
the x=0.6 data and may shed a light on the origin of the EMC effect.
