Ghost embedding

What is not excluded is recorded. A map that propagates the Cauchy data of $c$ from a surface crossing $W$ produces a nonzero free ghost; by (a) that ghost differs from $c$ near $W$, so the configuration on which the relative symmetry acts and the configuration in the carrier are different. Such a map is not an embedding of ${\mathfrak{F}}_W$'s ghost sector, its image is not in ${\mathfrak{g}}_W$, the relative identity (eq:relative) does not apply to it, and it lies outside the frozen contract. Whether the breaking functional vanishes on such ghosts is not decided here.