Normalization to the de Donder violation

This is an identity of whole response fields. A fixed smearing can vanish even when the response does not; the “if and only if” statement is not a universal nonvanishing assertion for every $f$.

When (eq:above) fails, the correct formula is still (eq:coordinate), including both the factor ${\sigma }_{\epsilon }$ and the layer term. The unrestricted tree remains defined, but the simplified double-integral normalization need not hold.