So, Bill, you like the true linear image better? I actually have created both a linear gamma working space in Photoshop as well as a ProPhoto RGB with a linear gamma so I could work with linear gradients in grayscale and color. But the original posted files WERE originally in linear until I transformed into sRGB for the original posting.
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Jeff, you already know most of what I am saying below, but others may be interested in the information.
The linear files do not display well without color management, because a gamma of 2.2 is assumed, at least with Windows. I don't know that much about Macs, but I understand they no longer use a gamma of 1.8. If you assign your custom ProPhotoRGB with a gamma of one to the linear file when you open it in Photoshop it will display with normal tonality, but the colors will be off unless your original has ProPhoto primaries. If you take a file with a bit depth of 12 and dump into a 16 bit linear space, it will still look very dark.
An alternative way of viewing a linear file in a gamma 2.2 or gamma 1.8 space is to apply a curve in Photoshop that undoes the gamma encoding. Shown below is a gamma 2.2 curve
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Here is the flower image at gamma = 1 on the left (in sRGB), with the gamma 2.2 curve applied in the middle, and with a contrast boost via an S-curve on the right. Simply applying a gamma of 2.2 results in a very flat image.
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Most HDR encodings use linear gamma without any tone curve (scene referred) and they display normally in Photoshop. If you want to reproduce a scene exactly, there must be a one to one relationship between the source (the scene) and the reproduction. When you view a gamma encoded file or print it, a reverse gamma function is applied but any compression is not undone, or else the image would clip due to limited dynamic range of the print or screen.