Why a cutoff is not substituted for the missing proof

Removing a neighborhood of ${\mathcal{N}}^{\circ }$ defines a smaller problem. A limit restoring that neighborhood needs an actual convergence or renormalized-limit theorem, its transverse degree, and its wavefront estimate.

No such limit is introduced. No cutoff triangle is assigned a value, and no subtraction supported on the characteristic set is added to ${\mathfrak{C}}_{\mathrm{part}}$. The class remains the one fixed in J0.