We have progressed in simulating the limits within which the Frary-Miller reconstruction gives acceptable results; most importantly, the number of photons emitted, knowledge of the bunch-bunch energy correlations, and angle cuts. We have also found which parts of the curve are most sensitive to the different parameters.
If it is possible to map these constraints to physical observables in the detectors, a clean centre of mass energy reconstruction can be found on a per-event basis. This will almost certainly also include finding finer causes of discrepancy between the true and reconstructed spectra.
If such observables cannot be found, there is the possibility of reverting to a statistical unfolding of the of the energy loss, whereby the distributions of all sensitive variables are compared and applied to the events.