Abstract

We give a supported realization of Cheung's Landmark X-G on the host retained by I-B and X-A-ST, with all analytical equations posed on its independently declared Minkowski completion. The regulator width remains fixed and positive.

An independent auxiliary field and one normalized gauge fermion produce the X-E/X-F Feynman-weight graviton operator. We compute the auxiliary–ghost Green matrix and prove that the off-shell nilpotent free differential preserves both the free equations and the graded causal relations. This constructs a free causal BRST derivation, not an interacting quantum BRST operator.

Two classical obstacles are then separated. The switched scalar action has an explicit natural gauge breaking, including an off-shell equation term outside $\mathrm{supp}\mathrm{d}g$, and a nonzero coefficient detected by a free scalar and a compact odd test. Independently, post-variation multiplication of gravitational sources by the onset violates variational reciprocity. A compact pure-gauge background in the onset layer gives the strictly positive free-solution pairing

It excludes an exact source-preserving variational upgrade on the unrestricted background class, even after free-shell-zero changes of representatives. The witness also admits free inputs with compact Cauchy data. Algebraic auxiliary elimination and corrections beginning at positive formal quantum order cannot remove it.

The direct three-tree background identity of X-F remains valid on the unchanged plateau algebra. Its survival is compatible with the upgrade obstruction because the two statements test different backgrounds and different maps. Local fish extensions, an exceptional scalar wavefront configuration, and a conditional background-independent loop addition are recorded without declaring the nonlocal one-loop observable constructed.

The principal free construction and obstruction are credited to X-G. The contribution here is their supported proof, normalization and causal-sign audit, and explicit separation of completion-level witnesses from laboratory support claims. These results provide a reproducible compatibility test for proposed quantum continuations, without claiming a universal obstruction to perturbative gravity. A finite supplied-evaluation interface has a complete destructive clock and reference-preserving regular transport. The release is local Grade S only.