  We conjecture an explicit formula for the image of a tensor product of
Kirillov-Reshetikhin crystals $\bigotimes_{i=1}^m B^{1, s_i}$ under the
Kirillov-Schilling-Shimozono bijection. Our conjectured formula is
piecewise-linear, where the shapes are given by the tropicalization of
cylindric loop Schur functions and the riggings are given by the
tropicalization of loop Schur functions. We prove that our formula changes the
riggings by the correct amount based upon the time evolution of the
corresponding box-ball system. We show that our formula is correct under the
column splitting portion of the Kirillov-Schilling-Shimozono bijection and for
$B^{1, s}$.
