Proposition: No cross-prescription repair

The ramp plateau identity, the convolution obstruction, and scalar-only negative readout closure are compatible. Neither the ramp nor its later scalar, tree, or free BRST/BV sheets changes the frozen convolution prescription by any operation constructed here.

Proof. The convolution obstruction follows from (eq:regulator)–(eq:preflight) and (eq:energy), without a ramp premise. The ramp identity concerns a different response map and supported algebra. The orbit theorem concerns the scalar family (eq:orbit), not every already invariant scalar.

The finite instruments act on declared finite inputs. None changes $w^{\mu }={\mathsf{E}}_0{\mathsf{C}}^{\mu }{T}_{g,\epsilon }h$, ${\mathsf{Co}}_1$, or either classical action prescription.