Remark

Lemma lem:index is the internal evidence for C1(i): the free metric index after cross-line contraction sits at $z$, which is the variable of XIV-G's residual test $G$, and the output is a symmetric contravariant tensor at $z$ (upper index pair $J=(ab)$), pairing with the covariant $G_{ab}$. The scalar slot at $y$ is the trivial line and does not change the rank. This is a reading of the displays, not a source identification; C1 remains a convention.