A compact audit of dependencies and non-identifications

The proofs use:

1. the explicit curvature convention and action;

2. algebraic density expansions and compact interior variations;

3. X-A's finite varied-action formula and divergence lemma;

4. the ordinary tensorial naturality of curvature and scalar stress;

5. the displayed linearized Bianchi identity;

6. classical Cauchy uniqueness and finite propagation for the optional compact-data witness.

They do not use an external graviton propagator, quantum Ward identity, counterterm catalogue, or response matrix.

The following objects remain distinct:

The first obeys the nonlinear fixed-background identity. The second includes gauge-fixing breaking. The third has the linearized Bianchi identity. The fourth is the gauge-fixed quadratic operator.

Similarly, a conserved Einstein source, a switched nonconserved source, and a source admitted by a gauge-fixed wave equation are not interchangeable. The witness distinguishes them at a lower order than any radiative or renormalization question.