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Yep, the projection function is supposed to give the closest point, although it doesn’t always have to be exact.  The sphere, plane, and box projection functions are exact, outputting the closest point on the surface of the object to the input.  Other functions are more approximate, like the möbius strip, intersection, and interpolation functions which give a somewhat close point (because the real projection fn is too complex).  I usually look at a shape’s 3D sdf first to get an idea of what the fn should roughly look like, then play around in 3d desmos and then extend to 4d from there.

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Alright, I'm going to see if I can generalize some regular closest point in 3d functions to 4d versions,  i got a capsule shape working, now im just seeing what else i can do