I go to one of these restaurants perhaps once every six weeks, and on each occasion I leave something like this. I've actually started to value it as an outlet for whatever's been rattling around my head at the time.

I love it. Sounds like you have fun (and they regularly get your money).

I think the general ontological category for center-of-mass is "derived fact". I'd put energy calculations about an object in the same category.

If the particles in the object contain 1000 bits of information, then the combined system of the object and it's center of mass contains exactly 1000 bits of information. The center-of-mass doesn't tell you anything new about the object, it's just a way of measuring something about it.

Or instead of bits of information, think about it in terms of particle positions and velocities. If you have an N-particle system, and you know where N-1 particles and the center of mass are, then you can figure out where the last particle is.

Regarding the note, in statistics you could call that a population parameter. While parameters that are used are normally things like "mean" or "standard deviation", the definition is broad enough that "the centre of mass of a collection of atoms" plausibly fits the category.

Ha, you mentioned that at the meetup, and I've remembered what I meant to say: you've read this classic Dennett paper, right? If I recall correctly (haven't reread it in years) it might be directly relevant.