The Hadamard matrix and the blocks of the cross-line

XII-A's frozen Hadamard data XIIAhad are $h_{\mu }=-W_{\mu }$ with

$h_{\mu }-{h_{\mu }}^{\mathsf{T}}=i{E}_{\mu }$, blocks

all other blocks zero; for the frozen translation-invariant data $H_{bb}=0$. An admissible replacement $H^{\prime }$ is defined by the four clauses of sec:fifthpass. The fourth pass shows that ${\mathcal{C}}_{\mathrm{cross}}$ is built from blocks named $H_{\gamma \gamma }$, $H_{\varphi \varphi }$ and replaced blocks (eq:cross); the fifth pass shows that the replaced blocks are not written $\hat{H}$ in any manuscript and that no manuscript equates them with XII-A's $H^{\prime }$. Whether XIV-J's replaced blocks are translation invariant (as the difference-variable pullback requires) is also not stated. The Hadamard data are T for XII-A's own objects and C as ingredients of (eq:cross).