  The proton elastic form factor ratio shows a discrepancy between measurements
using the Rosenbluth technique in unpolarized beam and target experiments and
measurements using polarization degrees of freedom. The proposed explanation of
this discrepancy is uncorrected hard two-photon exchange (TPE), a type of
radiative correction that is conventionally neglected. The effect size and
agreement with theoretical predictions has been tested recently by three
experiments. While the results support the existence of a small two-photon
exchange effect, they cannot establish that theoretical treatments are valid.
At larger momentum transfers, theory remains untested. This proposal aims to
measure two-photon exchange over an extended and so far largely untested $Q^2$
and $\varepsilon$ range with high precision using the {\tt CLAS12} experiment.
Such data are crucial to clearly confirm or rule out TPE as the driver for the
discrepancy as well as test several theoretical approaches, believed valid in
different parts of the tested $Q^2$ range.

Nuclear Experiment