  High precision measurements of the polarized electron beam-spin asymmetry in
semi-inclusive deep inelastic scattering (SIDIS) from the proton have been
performed using a 10.6 GeV incident electron beam and the CLAS12 spectrometer
at Jefferson Lab. We report here the first multidimensional study of single
$\pi^+$ SIDIS data over a large kinematic range in $z$, $x_B$, $P_T$ and
virtualities $Q^2$ ranging from 1 GeV$^2$ up to 7 GeV$^2$. In particular, the
structure function ratio $F_{LU}^{\sin\phi}/F_{UU}$ has been determined, where
$F_{LU}^{\sin\phi}$ is a twist-3 quantity that can reveal novel properties of
quark-gluon correlations within the nucleon. The impact of the data on the
evolving understanding of the underlying reaction mechanisms and their
kinematic variation is explored using theoretical models for the different
contributing transverse momentum dependent parton distribution functions.
