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.
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