  An amplitude analysis of the $K_{S}K_{S}$ system produced in radiative
$J/\psi$ decays is performed using the $(1310.6\pm7.0)\times10^{6}$ $J/\psi$
decays collected by the BESIII detector. Two approaches are presented. A
mass-dependent analysis is performed by parameterizing the $K_{S}K_{S}$
invariant mass spectrum as a sum of Breit-Wigner line shapes. Additionally, a
mass-independent analysis is performed to extract a piecewise function that
describes the dynamics of the $K_{S}K_{S}$ system while making minimal
assumptions about the properties and number of poles in the amplitude. The
dominant amplitudes in the mass-dependent analysis include the $f_{0}(1710)$,
$f_{0}(2200)$, and $f_{2}^\prime(1525)$. The mass-independent results, which
are made available as input for further studies, are consistent with those of
the mass-dependent analysis and are useful for a systematic study of hadronic
interactions. The branching fraction of radiative $J/\psi$ decays to
$K_{S}K_{S}$ is measured to be $(8.1 \pm 0.4) \times 10^{-4}$, where the
uncertainty is systematic and the statistical uncertainty is negligible.
