Internal vertices are not collapsed

The kernels $K_5,K_8,K_9$ already exist as tree-kernel pushforwards. Using them in a paired-symbol calculus would also require their own canonical relations, clean internal matching, symbol orders, and uniform remainder estimates.

No hidden vertex is set equal to $u_0$, $y_0$, or $x_0$. The present F2 audit requires none of those unproved internal symbol identifications.

Since the proposed final matching has failed its necessary clean test, this paper does not attempt those internal symbol constructions. The existence of the tree kernels is retained; a new symbol theorem for their composition is not inferred from it.