  Within the most recent extension of the quark-jet hadronization framework, we
explore the transverse-polarization-dependent dihadron fragmentation functions
(DiFFs) $H_1^\sphericalangle$ and $H_1^\perp$ of a quark into $\pi^+\pi^-$
pairs. Monte Carlo (MC) simulations are employed to model polarized quark
hadronization and calculate the corresponding number densities. These, in turn,
are used to extract the Fourier cosine moments of the DiFFs
$H_1^\sphericalangle$ and $H_1^\perp$. A notable finding is that there are
previously unnoticed apparent discrepancies between the definitions of the
so-called interference DiFF (IFF) $H_1^\sphericalangle$, entering the cross
sections for two-hadron semi-inclusive electroproduction, and those involved in
the production of two pairs of hadrons from back-to-back jets in
electron-positron annihilation. This manuscript completes the studies of all
four leading twist DiFFs for unpolarized hadron pairs within the quark-jet
framework, following our previous work on the helicity-dependent DiFF
$G_1^\perp$.
