User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191006023842/@comment-35470197-20191006033748

It would be good if I also had such intuitions which tell me the answer to questions which surpass mathematical open problems.

Anyway, even if we assume Inaccessible, ordinal analysis of that level will not be simpler. For example, if we work in ZFC set theory, the proof for the ordinal analysis of KPM level is very long. The large cardinal axioms which just ensure the existence of the corresponding ordinals are not so helpful in order to verify the comparison.