User blog comment:Dchew89/An Ordinal Describing the Growth Rate of my d(n) Function/@comment-30754445-20190218043613/@comment-30754445-20190218124205

"The most obviously applicable variation" is too vague to qualify as a valid mathematical definition.

And the final ordinal you'll get most certainly does depend on the progression you pick. Ideally, you'd want to get "as close as possible" to ωck1 from below, but the limit cannot be exactly ωck1 (because it is theoretically impossible to give a closed rule-set that generates a list whose limit ωck1). So the end result will depend on how strong your ordinal-building rules are.

And there's another thing to keep in mind:

If you plan to use your Δ0 in the FGH, you'll need to provide fundamental sequences for EVERY ordinal smaller than Δ0. Providing them just for the ordinals in your master-list is not enough. For example, calculating fΔ 0 (100) would involve fetching the 100th ordinal in the fundamental sequence of lots of ordinals (about fΔ 0 (100) of them), the vast majority of which won't appear on your list at all.