Evaluate XYZ additivity assumption

[Brankale]

Ideally, XYZ tristimulus values should be additive.

For example: XYZ_red + XYZ_green + XYZ_blue = XYZ_white

In practice, however, this equality does not hold for two main reasons:

Measurement errors

Due to instrument noise, calibration limits, and repeatability issues, we usually observe:
XYZ_red + XYZ_green + XYZ_blue ≈ XYZ_white

Display limitations

Even under ideal measurement conditions, many displays do not behave as perfectly additive systems, so:
XYZ_red + XYZ_green + XYZ_blue < XYZ_white

This effect is particularly noticeable on reflective displays. For example, on the Game Boy Advance it is common to observe:
XYZ_red + XYZ_green + XYZ_blue ≈ 0.9 × XYZ_white

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The first issue can cause problems when estimating the gamma curves of the three color channels, since even small measurement inconsistencies can result in significant gamma distortions under certain conditions. While mathematical correction methods can partially mitigate measurement errors, they do not fully address the problem.

A more robust solution is to measure the full XYZ tristimulus values (and, if possible, the spectral power distribution) across the entire red, green, and blue intensity scales.
This approach enables much more accurate and precise gamma estimation and also makes it possible to compute a reliable scaling factor for the grayscale.