The mask is feathered so the edge pixels are not fully masked in the feathered area. That's the nature of feathered masks. It's working as expected. If you don't want a gap, avoid feathering and use a hard-edge mask.
I'm sorry but I need a little more elaborate than "nature of it", from my view any thing inverted should be "Absolute" inverted.
Any feathered mask is a ramp from black to white in mask, from I gather the two grey areas (50% ramp) should coincide, but they dont.Could be to the number of steps being a odd number (as opposed to even), I really don't know so was hoping for a bit more technical reason why.
I do need feathered masks frequently and need to work with the inverted ones, my work around usually is to apply some more feather than needed and use Levels on both to displace them a bit.There can be other work-arounds thought, that's why I'm asking.
Feathering is a radius. With a 1 pixel feather, you actually have 2 pixels, one of each side of the edge. Hope that helps.
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I have a hunch (not tested) that it's because of grayscale gamma encoding. The mask is a grayscale image, as per your working gray.
I managed to spend some time testing and I'm fairly certain its not Gray Gamma settings, still don't know but the closest I could get is if you turn off "Blend RGB Colors Using Gamma X (where X is 1,00 as default) and use Color Space Gamma instead (mine being Adobe RGB that uses 2,2) the gap shrinks, doesn't'completely disappears but its noticeable smaller.
The "remaining" could boil down to anti-aliasing, don't know...