This project will create an advanced and general model of high-energy processes, focusing on the Large Hadron Collider at CERN. New analytical and numerical solutions will be developed and combined to reach unprecedented accuracy and detail. This will clarify important phenomenological questions in the Standard Model and will enable more precise searches for deviations from it (new physics). A publicly available numerical code will be produced, with a large number of applications. These include, for instance, precision extraction of fundamental parameters and improved absolute calibrations of experimental measurements, explicit theoretical modeling of new physics phenomena, and optimization of detector design and analysis strategies.