Poor-edge conjecture for normal colorings of bridgeless cubic graphs

Let $G$ be a bridgeless cubic graph. Let $\mathrm{NC}(G)$ be the set of all normal $5$-colorings of $G$, and, assuming this set is nonempty, let $\mathrm{poor}(G)$ be the maximum number of poor edges among colorings in $\mathrm{NC}(G)$. Let $P_{10}$ be the Petersen graph and let $P_{10}^{\Delta}$ be the graph obtained from $P_{10}$ by truncating one vertex. Poor-edge conjecture. If $G\ne P_{10}$, then

$$\mathrm{poor}(G)>0.$$

Moreover, if $G\ne P_{10},P_{10}^{\Delta}$, then

$$\mathrm{poor}(G)\ge 6.$$

The claim refines the Petersen Coloring Conjecture by predicting unavoidable poor edges in normal $5$-colorings, with stronger lower bounds away from the Petersen graph and its one-vertex truncation. The paper presents it as a proposed direction based on observations about small snarks and the constructions studied there.