Derivative placement and conservative bounds

In the independent charts,

Thus $s$ derivatives in $47$ and $t$ derivatives in $5a$ cannot reach the crossed coefficient. In $47$, ${\mathcal{B}}_{\mu }U=0$ and ${\mathcal{B}}_{\mu }V=-e_{\mu }$.

If $C^{\chi }$ has compact distributional order at most $h$, then for each multiindex $\gamma$,

This is the finite-order distribution estimate applied to translated differentiated profiles.

The resulting row bounds are

with

The maximal crossed derivative orders are $3,3,5,3,4,4,3$. The vertex contributes at most one crossed derivative; source $z$ derivatives cannot reach it. Finite mass of the localized seed measures completes the estimate.

The complete bound is $C_H{\delta }^{-h-13}\Vert \Phi {\Vert }_{5,H}$. It is a moderate bound, not a leading exponent or a Dini certificate. This distinction is also explicit in the supplied Em01-B estimate EmB.