Exact objective and corrected ending

The supplied X-G-ST constructs a normalized free auxiliary–ghost multiplet and proves an exact source-preserving variational upgrade obstruction XGST. Its parent is Cheung's Landmark X-G XG. The present manuscript continues the question of a restricted classical interacting structure without assuming that restriction automatically produces an interacting differential on the free causal carrier.

The distinction is substantive. An off-shell vector field can square to zero while failing to preserve the equations used to define a quotient. Section sec:descent gives an explicit example for the proposed nonlinear scalar transformation. Accordingly:

1. a relative local classical BV complex is constructed;

2. its identification with the unchanged free equation quotient is not made;

3. the natural proposed descent to that quotient fails already at first order;

4. no interacting quantum differential is released.

X-G supplies the principal normalization and reciprocity mechanism. X-F and the supplied X-F-ST supply the separate equation-level tree construction and its background identity XF,XFST. They are not reinterpreted here as variational Møller maps.

X-H-ST denotes this proposed manuscript. No parent X-H theorem, repository installation, registration, submission, acceptance, or successful compilation is assumed or asserted.