> The manifold in the video (if I am understanding correctly) is
> embedded in 4000 dimensional space. But we don't know the
> dimensionality of the manifold itself.

This is true.  It's possible that the cat manifold really does have 4000
dimensions, but perhaps more likely that it has fewer dimensions than
the embedding space, e.g., perhaps it's a 3,746 dimensional submanifold.
It's impossible to know.  We glossed over this in the video.

Also, 4,000 isn't exact either.  The algorithm uses a 64x64 latent image
which would give 4,096 pixels.

-- Dave