The supported plateau inventory and remaining boundaries

On an output plateau, ${A_{-3}}^{\mathrm{supp}}{|}_{U_0}=0$. The general supported inverse-quadratic tensor calculation is not completed by the isolated positive-placement calculation. For precision, its explicit radial-profile inventory is retained in Appendix app:plateau.

For the negative placement, on $a_0\le A\le \beta -a_0$, the two future cone equations give

Its exact measure is

Unlike $47$ and $5+$, $u$ remains integrated. The $u=0$ trace theorem is not a theorem for this sector. At non-tip $A$, $u=O(\delta )$ gives $Z=O(\sqrt{\delta })$; if $A=O(\delta )$ as well, the equation instead gives $Z=O(\delta )$. The intermediate regimes and endpoint matching remain separate obligations.

The outstanding tasks for a global complete-family expansion are:

1. evaluation of the supported plateau tensor inventory;

2. lower coefficient evaluation of $47$;

3. the complete negative-placement asymptotic;

4. residual-tip and non-tip overlap cancellation;

5. common-coordinate complete scale assembly and a vanishing compact-uniform remainder.