Proposition: Invisible defects outside the canonical domain

If $r{F}_0=c$, then $r{F}_0(A)=0$ for every $A\in H$. This does not in general imply $F_0(A)=0$ on $W$.

Proof. The first assertion follows from $c{|}_H=0$. If $p\in W\setminus O$ and the residual bundle has a nonzero fiber there, a nonzero delta distribution at $p$, with a chosen fiber coefficient, restricts to zero on $O$. Thus restriction need not detect a defect supported outside $O$.