In this study, we demonstrate that the recent measurement of azimuthally collimated, long-range rapidity ("ridge") correlations in √s=13 TeV proton-proton (p+p) collisions by the ATLAS Collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high-energy QCD. The observation that the integrated near-side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semihard saturation scale in the color glass condensate framework. We argue further that the azimuthal structure of these recent ATLAS ridge measurements strongly constrains hydrodynamic interpretations of such correlations in high-multiplicity p+p collisions.