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We show that the dominant channel proposed for the determination of the Higgs boson trilinear coupling, pp arrow right HH+X via gluon fusion, exhibits an interference structure that is independent of the collider energy for collider energies in the range 8 TeV[< or =]s[< or =]100 TeV and is almost maximally destructive. This insensitivity to the collider energy remains approximately true for a variety of other two Higgs production mechanisms although the magnitude of the interference varies widely.