ADDENDUM:
Here's the link to Natsugou's paper: (Tetration Forum 2023) Negative ranks hyperoperations (new pdf)
And here's more discussion about defining zeration and negative rank operations: (Tetration forum 2022)How could we define negative hyper operators?, also in that thread look for the reference to Tencer's post on MSE [2015 Tencer].
Here's the link to Natsugou's paper: (Tetration Forum 2023) Negative ranks hyperoperations (new pdf)
And here's more discussion about defining zeration and negative rank operations: (Tetration forum 2022)How could we define negative hyper operators?, also in that thread look for the reference to Tencer's post on MSE [2015 Tencer].
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)