Zeon formulation of Ryser's conjecture I

Let $\Gamma$ be the zeon incidence representation of an $r$-uniform $r$-partite hypergraph. Let $\gamma$ be the zeon element

$$\gamma=\sum_{\{I: \zeta_I\Gamma=0\}}\zeta_I.$$

Here $\natural\gamma$ denotes the minimum grade of $\gamma$, and $\kappa(\Gamma)$ denotes the index of nilpotency of $\Gamma$.

Zeon formulation of Ryser's conjecture I. One has

$$\natural\gamma\leq (r-1)(\kappa(\Gamma)-1).$$

This is presented as an equivalent zeon-algebra formulation of Ryser's conjecture, and is open together with the underlying hypergraph conjecture.