Finite information is not a complete boundary operator

A fixed tripartite qubit process is a $64\times 64$ Hermitian matrix. All its one-use probabilities are linear functionals of finitely many real coordinates. Infinitely many instrument settings do not create infinitely many independent process coordinates.

This observation alone is not a cardinality proof excluding every imaginable map from process matrices to metric classes. The proved obstruction is Theorem thm:finite-mode, with its explicit linear-amplitude hypotheses. A general inverse identification claim requires its own observation law and comparison class.