Rigney, you can't pump anything to an absolute negative pressure, just like there is no temp below absolute zero. You cannot pump the vacuum out of anything, it genuinely doesn't make sense... I understand that you are asking what is a vacuum and i think it's a viable question but you can't pump out the vacuum, at least not in the context of modern physics.
The question of what is the vacuum is a reasonable question, a recent article in Discover magazine show casing the works of Julian Barbour has some interesting ideas about Space and what it is. He is trying to overturn Einstein, his ideas are interesting but way beyond me mathematically but the concepts are not impossible to grasp. If I understand them correctly he doesn't even think the concept of space time is correct, no 4th dimension and space is just ... space...
http://platonia.com/papers.html