User blog comment:DrCeasium/Continued hyperfactorial array notation/@comment-5529393-20130327230302

Your starting function seems somewhat unnatural - why start at \(x_1\), then go to \(x_1 -1\), then switch to \(x_2 - 1\)?

Your notation is not in a "completely new direction". Actually, it is exactly array notation, except for a couple of functions which don't matter to the growth rate. So Hyperfactorial Array Notation is not more powerful than Bowers' Array Notation, it has the same strength. For your notation to be notable, it can't just use the same underlying structure as a previous one with a couple new functions to make it seem different.

I'm not trying to be a Debbie Downer here, I wish you the best in continuing your notation. But it needs more originality.