Formal and numerical parameters

The nilpotent $\epsilon$ in (eq:jet-observable) belongs to $\mathbb{R}[\epsilon ]/({\epsilon }^2)$. The real $\lambda$ in the product obstruction is a parameter in an exact degree-one polynomial.

The pilot probabilities use real finite matrix entries. They do not substitute a dual number into a density matrix. First-order jet coefficients may be separately encoded as real settings on a finite classical catalogue.