I thought a quantum was a semantic construction used to define a discrete unit of energy. Its a convention, not a hard fast physical unit. Maybe you could define a quantum first, I'm a little confused on the question.
You kinda lost me on that, Loren. As Order pointed out, a quantum is essentially the smallest possible unit of... something. A quantum of EM is a photon, a quantum of time, if such exists, would be a (chronon?), a quantum of gravity, if it exists, would be a graviton. I don't think that your question, as asked, is answerable.
I think of a quantum as having foremost the minimum measurable amount of action, h. Aren't any other "quanta" observed (such as those constrained to quantum gravity, like the Planck units, or free particles, like those of the photoelectric effect) - including structure - more secondary to the process of measurement?
One of the more interesting personal sites I have seen in a while. I believe I can understand enough of it to recognize some connections to my initial inquiry. The article offers primarily a review of various advanced mathematics used to describe quanta in visualizable terms. (John Archibald Wheeler has been concerned about pregeometry as a substructure of quantum gravity for quite some time.)
At first read I wonder what Micho Durdevich would think of quantum geometry as a projection of spacetime onto a discontinuous, exactly 3-dimensional (yet fractal) phase space - that is, one both probabilistic and embeddable?