  The exploration of the fundamental structure of strongly interacting matter
has always thrived on the complementarity of lepton scattering and purely
hadronic probes. As the community eagerly anticipates a future electron ion
collider (EIC) in the U.S., an outstanding scientific opportunity remains to
complete "must-do" measurements in p+p and p+A physics in the years preceding
the EIC. As we describe in this document, these measurements will be essential
to fully realize the scientific promise of the EIC by provid-ing a
comprehensive set of measurements in hadronic collisions that, when combined
with data from the EIC, will establish the validity and limits of factorization
and universality. The outlined program will on the one hand lay the groundwork
for the EIC, both scientifically and in terms of refining the experimental
requirements for the physics program at the EIC, and thus be the natural next
step on the path towards an electron-ion collider. On the other hand, while
much of the physics in this program is unique to proton-proton and
proton-nucleus collisions and offers discovery potential on its own, when
combined with data from the EIC it will provide a broad foundation to a deeper
understanding of fundamental QCD.
