Corollary: What the witness does and does not cancel

For every shell-descending slot rule in the class,

For the admitted cochain of Section sec:kernel,

Nevertheless that cochain is not an integrated compensating functional in the frozen class.

Proof. The first assertion is (eq:Y-zero). The second is (eq:C-cancel). The lack of an integrated realization follows from Theorem thm:obstruction, or directly from ${\bar{\delta }}_{\theta }\bar{F}=0$.