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It is known that multiple partonic scatterings in high-energy proton-proton($pp$) collisions must happen in parallel. However, a rigorous parallelscattering formalism, taking energy sharing properly into account, fails toreproduce factorization, which on the other hand is the basis of almost all$pp$ event generators. In addition, binary scaling in nuclear scatterings isbadly violated. These problems are usually ``solved'' by simply not consideringstrictly parallel scatterings, which is not a solution. I will report on newideas (leading to EPOS4), which allow recovering perfectly factorization, andalso binary scaling in $AA$ collisions, in a rigorous unbiased parallelscattering formalism. In this new approach, dynamical saturation scales play acrucial role, and this seems to be the missing piece needed to reconcileparallel scattering with factorization. From a practical point of view, one cancompute within the EPOS4 framework parton distribution functions (EPOS PDFs)and use them to compute inclusive $pp$ cross sections. So, for the first time,one may compute inclusive jet production (for heavy or light flavors) at veryhigh transverse momentum ($p_{t}$) and at the same time in the same formalismstudy flow effects at low $p_{t}$ in high-multiplicity $pp$ events, makingEPOS4 a full-scale ``general purpose event generator''. I discuss applications,essentially multiplicity dependencies (of particle ratios, mean $p_{t}$, charmproduction) which are very strongly affected by the saturation issues discussedin this paper.

Revealing a deep connection between factorization and saturation: New  insight into modeling high-energy proton-proton and nucleus-nucleus  scattering in the EPOS4 framework