Exact release and necessary corrections

release and necessary corrections{ A relative classical BV deformation is constructed through order ${\kappa }^3$, meaning modulo ${\kappa }^4$. Its finite supplied reports have complete instruments.

X-H-ST already contains nonlinear classical interactions. Accordingly, this paper is not advertised as the first classical interacting construction. Its new step is an explicit compact third-order scalar vertex and the associated finite-order and instrument audit.

Free field BRST recovery holds at $\kappa =0$. Full free BV recovery additionally requires the centered background sector specified below. No interacting differential on the unchanged free causal carrier is inferred.}