Nonvanishing of the total face color polynomial for bridgeless graphs

Let $G$ be a bridgeless connected graph and let $\Gamma$ be a signed ribbon diagram of $G$. For $n$ a positive integer, write $T(\Gamma,n,t)$ for the total face color polynomial. Total face color polynomial nonvanishing conjecture. The polynomial $T(\Gamma,n,t)$ is nonzero. This is presented as a stronger form of the cycle double cover conjecture. The theorem immediately preceding it establishes an equivalence between nonvanishing and the existence of a cycle double cover for bridgeless connected trivalent graphs, while the asserted extension to arbitrary bridgeless connected graphs remains open.