Energy sharing and dissipation between fragments at scission
In plain words
The energy released in fission ends up partly as the motion of the fragments and partly as heat inside them, and the light and heavy fragments get different amounts of heat. How much energy is turned into heat on the way to scission, and why extra input energy goes mostly to the heavy fragment, are not understood from first principles.
Precise statement
For $235\mathrm{U}(\mathrm{n},\mathrm{f})$ and $239\mathrm{Pu}(\mathrm{n},\mathrm{f})$, determine the partition of the total excitation energy TXE (approximately 20 to 30 MeV) between light and heavy fragments as a function of fragment mass, and the fraction of collective energy dissipated into intrinsic excitation between saddle and scission. The answer must reproduce the sawtooth of prompt neutron multiplicity $\nu(A)$ and its change with incident neutron energy, where added excitation appears mainly in the heavy fragment.
What would settle it
A microscopic dynamical calculation, with no parameters fitted to neutron multiplicities, that reproduces $\nu(A)$ and its incident-energy dependence for at least two actinides.