Sector obligations and residual scaling

A calculation must cover, with overlap control:

1. the complete supported seed ${\mathcal{P}}_{\mathrm{supp}}$, including both root terms;

2. the $K_{47}$ two-cone seed;

3. the two $K_5$ placements separately;

4. their cone-tip transitions;

5. complementary compact regions and noncompact rescaled tails.

Equations (eq:residualcones)–(eq:residualconstraint) are exact input for this task. They do not show that $A_r$, $B_r$, and $Z_r$ have common scale weights.

The alignment equations in $(a,b,y)$ do not themselves impose $r=0$. For example,

contains points with nonzero $r$; the $K_{47}$ support then imposes its additional $b-z$ cone. Therefore the codimension-eight marked locus $N$ must not be declared an exhaustive singular set merely from the cone-rank calculation. The residual intersections also require analysis.

For the supported rows, $r=0$ is exact. For the other rows, fixed compact $r$-support can become unbounded after rescaling. Compact support of $\rho$ alone does not estimate these tails.

No exhaustive scale-sector decomposition or quantified characteristic remainder has been completed here. The exact regrouping is the starting expression for that calculation.