The azimuthal collimation of di-hadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the Color Glass Condensate (CGC) effective theory [1] by N 2 c suppressed multi-ladder QCD diagrams that are enhanced α −8 S due to gluon saturation in hadron wavefunctions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger di-hadron yields and predict further systematics of these yields with varying trigger pT and charged hadron multiplicity. Radial flow generated by re-scattering is strongly limited by the structure of the p+p di-hadron correlations. In contrast, radial flow explains the systematics of identical measurements in heavy ion collisions.The discovery of di-hadron correlations in high multiplicity proton-proton collisions [2], long range in the angular (pseudo-rapidity) separation of the pairs relative to the beam axis and collimated in their relative azimuthal angle about this axis, provides significant insight into rare parton configurations in the proton and their dynamics in hadronic collisions.High multiplicity proton-proton collisions select "hot spot" configuations of wee gluon states in each proton. Quantum Chromodynamics (QCD) predicts that such hot spots have a maximum occupancy of order α −1 S [3, 4] (α S being the QCD fine structure constant), and have a typical size ∼ 1/Q S , where Q S is a dynamical saturation scale. This scale grows with the energy and centrality of the collision; when Q S ≫ Λ QCD , the fundamental QCD scale, highly occupied hadron wavefunctions can be described using weak coupling methods.A weak coupling effective field theory (EFT) that describes high density wee parton configurations in the proton is the Color Glass Condensate (CGC) [5]. When CGC's shatter in a high multiplicity collision, multiparticle production is a consequence of approximately boost invariant radiation from "Glasma flux tubes" of transverse size 1/Q S [6]. Multiplicity distributions [7] derived from factorization theorems [8] in this framework are in good agreement [9,10] with recent LHC data [11]. Long range rapidity correlations of gluons computed in the CGC EFT [12] were previously shown to be in qualitative agreement [1] with the CMS di-hadron correlation data.A source of long range rapidity correlations in hadronhadron collisions are back-to-back gluons emitted from a single t-channel gluon ladder; another source, called "Glasma graphs" are gluons emitted from two separate ladders. Representative graphs of each are shown in fig. (1). In the "dilute" high p T perturbative limit of QCD, the back-to-back contribution is dominant. However, at high parton densities, when Q 2 S ≫ Λ 2 QCD , and p 2 T ∼ Q 2 S , the effective coupling of gluons in ladders to strong color sources at higher rapidities changes from g → 1/g. This corresponds to an enhancement of Glasma graphs by α −8 S compared to the α −4 S enhancement of the back-to-back graphs. Equally important are the very different a...