Therefore, the most logical proposition is that there is a mass not described by the standard model which can be converted to energy by waves and which can convert the energy of wave back to mass and which tends to preserve conservation of energy and mass.

The problem is that the equation e=mc^{2} in fact should be written E=dmc^{2 }where dm is the derivative (or in simple cases the delta of two masses). E is always photon(phonon) energy. In SO(4) physics the energy mass relation is much more complicated. Already R.Mills found the conversion factor for photon energy to nuclear mass. It is of course different from the stone age formula. But real (EM-) mass stored in atoms does 2,3,4 (2x2) or 5 rotations. All these masses are not conform with E=mc^{2}. You need to apply the metric factor for a conversion to photon mass.

If you use such a proper conversion you can directly calculated gamma levels (energy) of some simple isotopes .