When you say a)"rarified" and b)"squished" do you mean...

Ultimately I mean lower pressure and higher pressure. Specifically I am
talking about the extra pressure that is distributed across the entire
earth's surface while the airplane is flying. Two things are being
disscussed here - what keeps the airplane up, and what is ultimately
supporting it; I was addressing the latter.

By "flow upwards a sufficient amount" I presume you are
thinking about some sort of density variation changing the
volume of air below the wing that is later released?

Yes, though I am not talking just about the air immediately below the
wing, but of all the air that is pressing against the earth. The thing
that prevented this (net) upward flow while the plane is flying is the
continued downflow from the wing. Once that stops, the air can spring back.

This concept of "springing back" implies both pressure and
density changes. While it's true that gas does change
volume and density when pressure is applied, when studying
the phenomenon of lift at subsonic speeds, we usually ignore
the density changes.

Yes, and that is a good approximation for some analyses. It does leave
something out though, and sometimes the thing that is left out is the
answer being sought. When I jump up, I push the earth down. This can
usually be ignored, but it is necessary to complete the analysis of all
the forces and their conservation. On a larger scale (the moon orbiting
the earth) it becomes significant.

If this is a discussion about lift ( I apologize if it's not
:-) and not just a pure discussion of the physics of a
compressible gas, it's not clear to me why you would want to
consider compressible effects. It's pretty universally
agreed we can ignore them.

The contention is that there is =no= net downflow. That contention is
not true (although it's "pretty close"). The difference between "no"
and "almost no" is what holds the airplane up.

But of course, it doesn't have to compress (at least not in
theory) and when you sit on a rock, the extent to which it
does compress is so small we can easily ignore it.

Well, actually it does have to compress. That's the source of the
force. Even a rock compresses. We can ignore it for most practical
purposes, but not when you are asking where the force comes from. And
that is the question being addressed.

Jose
--
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