Theorem: Free-multiplet release

For the XI-A quadratic normalization and the conventions of Section sec:handoff, the following are established.

1. One gauge fermion yields the frozen term $S_{\mathrm{gf}}=\int D_{\nu }{D}^{\nu }$ after auxiliary-field elimination.

2. The full free operator has unique retarded and advanced Green operators on compact interior sources, with the stated causal support.

3. The free differential is nilpotent off shell with the auxiliary field retained, and descends to the causal polynomial field algebra.

4. The plateau algebra has zero intersection with residual de Donder gauge.

5. The regulated first coordinate coefficient of a classical de Donder field is a propagated layer functional.

These statements do not construct an interacting or relational BRST cohomology class.