Remark: Eight third-order double-plateau variational directions

In the double-plateau reading the SA subspace has dimension $12$ at total derivative degree $D=3$, of which $4$ lie in $\ker \mathrm{Collapse}$ (hence contribute $0$ to the variational image) and $8$ survive in ${\mathcal{T}}_{\mathrm{variational}}\cap \mathrm{im}\mathrm{Collapse}$. Each of the eight image directions collapses to a pure third-order operator on the residual field $h$ (every monomial in the collapsed tensor has field multi-index of order exactly $3$; no undifferentiated or second-order $h$ terms). They arise from $N=2$ coherent contact assignments with $|\gamma |=1$ (and linear combinations thereof), not from $N=4$ ultralocal potentials. They are not gravitational scalar counterterms. In particular they are not Euler tensors of $\int R$, $\int R^2$, $\int {\mathrm{Ric}}^2$, or of any other Lorentz-scalar curvature polynomial at this order: those live in the $D=0$ ultralocal block or the $D=2$/$D=4$ matched curvature-squared sector of Proposition prop:match. The eight directions are variational collision tensors of total derivative degree $3$ inside the selected double-plateau image; their functional interpretation (if any) is deferred to the M.5 ledger and is not claimed here. Exact sparse SA supports are recorded in helmholtz_certificates.txt (double_plateau, $D=3$).