Four inherited boundaries

inherited boundaries{

1. IX-A supplies the carrier ${\mathcal{P}}_{\Sigma }$ and topology ${\tau }_{\Sigma }$. It admits $B_f$ and the selected two-factor contraction with $W_g$; it does not construct or assign the triple after either sharp association.

2. VII-C supplies the logarithmic divergence, the separated-support witness, and the normal-topology obstruction under its extension requirements (E1)–(E4).

3. VII-D supplies the strong numerical finite part, the parent conversion class $\mathbb{R}r$, and the rate controlled by $p_{K,64}$. This is a numerical prescription, not a quantum algebra construction.

4. None of these sources supplies the second sharp multiplication. No such multiplication is defined here.

}