Theorem: Collapse of C anom ; unmatched remainder retained

Assume Gate V. Let $C_{\mathrm{anom}}$ be as in Definition def:M6-Canom (unit $r=1$ for the linear probe; overall factor $r$ restores the physical coefficient).

1. {Formal / $\chi$-plateau.} $\mathrm{Collapse}(C_{\mathrm{anom}})$ is nonzero (744 nonzero keys) and not self-adjoint ($\mathrm{SA}$-defect nonempty). It is therefore not a nonzero variational tensor.

2. Preparation / double plateau. $\mathrm{Collapse}(C_{\mathrm{anom}})=0$. Structural reason: the $S^2$ coefficient $\hat{a}$ is supported only on $|\partial {\sigma }_{\epsilon }|=2$ ($C_2$ sector); both plateaus set ${\sigma }_{\epsilon }\equiv 1$ and kill those derivatives.

3. Matched projection (double plateau). The orthogonal projection of $\mathrm{Collapse}(C_{\mathrm{anom}})$ onto $\mathrm{span}\{E_{R2},E_{RC2}\}$ (the M.5 matched Euler tensors) is $(0,0)$, since the vector itself is $0$.

4. Unmatched remainder. In the double plateau the remainder is $0$. In the formal reading the entire non-self-adjoint $\mathrm{Collapse}(C_{\mathrm{anom}})$ is retained as unmatched remainder. No unmatched component is discarded and renamed “the anomaly.”

Proof. Exact collapse columns and SA defects: scaling_anomaly.py (reads the same $\bar{a}$ and Collapse as M.4). Linear independence of $E_{R2},E_{RC2}$ and vanishing of $\mathrm{Collapse}(C_{\mathrm{anom}})$ in the double plateau give the projection claim.