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The physics content of the QGSJET-III Monte Carlo generator of high energyhadronic collisions is described. In particular, a phenomenologicalimplementation of higher twist corrections to hard parton scattering processesis discussed in some detail. Additionally addressed is the treatment of theso-called ``color fluctuation'' effects related to a decomposition of hadronwave functions into a number of Fock states characterized by different spatialsizes and different parton densities. Selected model results regarding theenergy-dependence of the total, elastic, and diffractive proton-proton crosssections are presented.

QGSJET-III model of high energy hadronic interactions: The formalism