Validate whether recovered posterior modes are genuine degenerate solutions

Establish whether all composition and grain-size modes recovered by TNFlow correspond to genuine degenerate solutions by resynthesizing each mode through the Shkuratov radiative transfer model and comparing the resulting spectra with the input spectrum.

Background

TNFlow produces multimodal posterior distributions over TNO surface compositions and grain sizes, and the authors identify multiple distinct solutions for most synthetic test and out-of-distribution spectra. Although the posterior often contains a mode close to the true composition, the reported mode search alone does not demonstrate that every recovered mode is physically valid or spectrally equivalent to the input.

The proposed unresolved validation is to pass each recovered mode through the forward Shkuratov radiative transfer model and compare the synthesized spectrum against the original spectrum. This would determine whether the modes represent genuine inverse-problem degeneracies rather than spurious posterior solutions.