Abstract

We construct a relative classical Batalin–Vilkovisky structure and finite destructive-readout interfaces on the supported host retained by I-B and X-A-ST. All analytical fields and Green operators remain on the declared Minkowski completion, at fixed positive regulator width.

On the plateau, the X-G-ST field multiplet admits an explicit nonlinear differential $s=s_0+\kappa s_1+{\kappa }^2{s}_2$ that is nilpotent off shell. A parity-checked antifield lift and the natural Einstein–scalar reference action give a classical master action through order ${\kappa }^2$, as a local variational identity modulo divergences. The auxiliary field remains independent. The construction retains background tadpoles rather than deleting terms needed by the action identity.

Two corrections determine the scope. First, nonlinear nilpotence does not imply descent to the unchanged free equation quotient. A compactly tested free-solution witness shows that the natural first-order scalar transformation does not preserve that quotient. Consequently the relative classical complex is not an interacting differential on X-G-ST's free causal algebra. Second, the positive reciprocity pairing of X-G is a ghost-number-zero obstruction to an exact source-preserving variational upgrade, not the ghost-number-one classical master-equation residual. Both distinctions are proved rather than imposed terminologically.

We define finite dictionaries of supplied coefficient evaluations and construct separate complete destructive instruments for classical residual reports and for the reciprocity witness. Their output includes the classical code and the unmeasured finite residual, with arbitrary untouched references retained. The instruments report installed evaluations; they neither acquire continuum fields nor turn an odd BV residual into a physical field observable.

A first-order quantum correction is formulated only as a conditional consistency problem. Local fish ambiguities can be encoded once specified, but the missing nonlocal contraction and an interacting quantum BRST theorem are not supplied. The contribution is a controlled separation of local classical closure, free-carrier descent, variational integrability, and complete report implementation. This provides explicit tests against false upgrades while preserving the earlier tree identity. The release is local Grade S, not spacetime emergence.