See https://googology.fandom.com/wiki/User_blog:DaVinci103/%CF%86_%E2%86%92_%CF%88_%E2%86%92_%E4%B8%89_%E2%86%92_%E4%BA%8C_%E2%86%92_%E2%88%9E for my latest attempt at creating this notation.
This is an attempt at understanding 三関数, googology.fandom.com/ja/wiki/ユーザーブログ:P進大好きbot/ヴェブレン関数→ブーフホルツのψ関数→? #googology