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All y'all need to take some information theory classes.
The reason you cannot create a perfect LUT is that when you map the spectrum of the incoming light onto RGB channels, the information which specific wavelengths the incoming light was composed of is lost. This makes it impossible to predict which color a film photo would have produced (unless the sensitivity curves had the same shape)
If you look at picrel for example, a 40% (of some arbitrary unit) exposure at 600nm would yield the very same "R" value as a 100% exposure at 650nm. The film on the other hand is much more sensitive at 650nm and would yield ~10 times more cyan (which becomes red after inversion) at the latter exposure. You have no way of telling that from the digital image.
This has nothing to do with linearity or dynamic range whatsoever.