We can embed a discrete state into a contiuum theory and describe those states as equivalence classes of states in that theory.
Cylindrical consistency ensures that the result of a computation (e.g. an inner product, an expectation value) does not depend on which representative one chooses. This gives us a contiuum theory!
Huggett: where does the cylinder come in? Artefact from QFT!
How do we embed? embeddings should be determined by the dynamics of the theory; and fine- and coarse graining should play a role!