User blog comment:Sbiis Saibian/The Great Googology Census of 2016/@comment-24509095-20160125035242/@comment-5982810-20160125041635

This appears to be googological in nature:

http://googology.wikia.com/wiki/User_blog:King2218/Infinite_Extensibility

It also appears that you were trying to invent something new even if it technically matched BEAF with an alternative notation. So you would qualify conditions (1),(3),(4), and (5). Did you consider yourself a "googologist" at any point in the past?