The three-tree plateau is retained once

The parent identity and its kernel-admission hypotheses remain those of X-F/X-F-ST XF,XFST. The proposition does not derive those kernels again, add their coefficients a second time, or identify their source response with a variational BV realization.

In particular, no observable BV-closure theorem follows from (eq:trees). No equality of different quantum ordering presentations is assumed.