The excluded edge gap and switch dependence

The condition in Proposition prop:edge is conditional: not every frozen switch has an interaction plateau in the ramp zone. If it does not, the switch terms in (eq:var1)–(eq:var2) must also be retained.

A nonzero integrated coordinate gap does not prove a nonzero total smeared free class for every fixed $f,g$. A test may miss it, its resulting representative may be an equation zero, or switch contributions may also enter. Likewise, $-L_{1,g}[h^{\prime }]{\mathsf{E}}_{\mathrm{A}}{\theta }_1$ need not be nonzero on every datum and is not the whole second defect.

If a genuinely nonzero order-$\kappa$, order-${\hslash }^0$ total defect has been established, a correction beginning at ${\kappa }^2$ or at positive $\hslash$-order cannot remove it while that lower-order prescription remains fixed. The coefficientwise reason is the same logical pattern as VI-B's order obstruction, not an identification with its defect VIB.