Any RAW histogram should have subdivided f-stops indicated on it (at least for the top 3 or 4 stops). That's a given. The vertical marker lines would have different spacings for linear, gamma, and logarithmic (f-stop) displays.

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The spacing for linear and gamma encoding can be deomonstrated by the Photoshop histograms of a Stouffer step wedge. The patches vary by 0.1 in density units, or 1/3 stop per patch. In the linear encoding, the first 3 patches (1 f/stop) occupy the right half of the histogram, the next stop the next fourth of the histogram, etc.

In the gamma encoded data, the distribution of the f/stops is more uniform, but there is still compression on the left. As you pointed out previously, this is a power function.

If one could plot the log base 2 of the exposure, the desired f/stop display would result, but I don't know of a way to do this in Photoshop.

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When does changing the axis of a chart between linear, logarithmic, or gamma-adjusted ever change the nature of the data?

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The underlying data are not changed. However, if you apply a log scale to the graph, this is the same as applying a log transformation of the data and plotting on a linear scale--one has effectively applied a transformation with the use of the log scale.

By your reasoning, a linear raw image and a gamma transformed image are the same, since the underlying raw data have not changed. However, they have a quite different appearance. Again, sematics and I would not press the point.