The actual local source kernel

The theorem includes the ${\sigma }^{\prime \prime }{C}_2$ and ${\sigma }^{\prime }{M}_2$ kernels, not only the $\sigma J_3$ kernel. The proof is an explicit product–pushforward calculation; it is not an inference from smoothness of the response. There is no failed collinear product hypothesis to reinterpret as a no-go.

The bound is special to this finite Minkowski composition: constant fiber maps, translation-invariant Green kernels, local differential vertices, and smooth external weights supply covector balance. No corresponding theorem for an arbitrary nonlocal or curved-background kernel is claimed.

This admission concerns the changed functional (eq:CD). It does not supply a new representative of XI-G's original excluded shell class.