Standard mathematical context

The local variational BV framework and its distinction between off-shell complexes, equations, and observables are standard FRBV. Perturbative quantum gravity requires additional product, renormalization, and quantum master-equation constructions BFR. Those additional operations are not supplied by the classical bracket used here.

The underlying scalar polynomial and BV construction are not claimed as new general techniques. The contribution is their explicit supported continuation with a finite-order residual calculation and a complete finite-report interface.