The representation forced by the frozen class

This specifies the representation before any cocycle test: every successful shell-descending proposal in the frozen class has the trivial module action. The zero off-shell rule realizes this representation, so the conclusion is not based on an unconstructed action.

The theorem uses the simultaneous requirements of causal zero-past output and free-shell tangency. It does not state that every retarded response vanishes. A sourced response generally fails the homogeneous tangent equations.

Nor does it state that every action on free Cauchy data is trivial. An action with nonzero past data or an unpropagated nonlocal component lies outside the frozen class.