User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191006023842/@comment-31580368-20191006041703

My main assumption is based on the fact that cardinals are characterized by the similar recursive transformations as a large counable ordinals. So for example we can build a hierarchy of gap-ordinals with Σ_n elementary substructure like hierarchy of stable ordinals with П_n-reflection. And further... we can build a hierarchy of gaps of cardinality with Σ_n correctness like hierarchy of gap-ordinals with Σ_n elementary substructure.