User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-30004975-20180116061613/@comment-30004975-20180116175548

Why? M diagonalizes over I(...), 1M (1-weakly Mahlo) diagonalizes over M(...), 2M diagonalizes over 1M(...), and K diagonalizes over (...)M. Then K(1,0) diagonalizes over K(a), 1K diagonalizes over K(...), something diagonalizes over (...)K, something else diagonalizes over the arguments of something, etc. The I, M, and K layers behave similarly enough that they could probably be diagonalized.