Declarations

scope. All fields and products in this manuscript are smooth classical coefficient fields. The metric is an independent classical configuration variable, not a quantized field.

correction. The title refers to an empty fixed-input Einstein jet. Gauge fixing is not claimed to preserve the invariant action's Noether identity. The full Einstein action is specified because nonlinear classical identities cannot be certified from the quadratic coefficient alone.

. No successful pdflatex execution, proof-assistant verification, independently checked symbolic calculation, or referee review is asserted. No empirical data or numerical graph calculation is used.

work. A free multiplet, gravitational propagator, ghost and antifield sector, BRST identity, quantum state, relational product renormalization, tree calculation, and sharp-ramp or adiabatic limit remain separate tasks.