This is an implementation of primitive sequence system (PrSS). It works as follows: At the beginning, the list (ε) is set to [8, 7, 6, 5, 4, 3, 2, 1, 0]. This list represents an ordinal, it currently represents the ordinal ω^ω^ω^ω^ω^ω^ω^ω (ω↑↑8), and it evaluates this ordinal on the Hardy hierarchy (it's thus ω↑↑7 on the FGH). The list is a PrSS list backwards, as backwards PrSS is easier to implement. To evaluate this ordinal with the Hardy hierarchy, the following is repeated until ε is empty, and thus represents the ordinal 0: my variable is increased by 9, my variable represents the argument (or base) of the Hardy hierarchy. Then, n is set to the first element of ε. I use the variable n twice, meaning I save a use of a number with this. If n = 0, ε represents a successor ordinal, and thus the first member of ε (n) is removed from ε. Otherwise, ε represents a limit ordinal, and ε[n] is calculated as follows: j is set to the index of the first occurrence of n - 1 in ε, this is easier than looking for the first member <n in ε as Scratch has a built-in block for this. This is also why ε starts as [8,7,6,5,4,3,2,1,0] as opposed to simply [8]. Then, the first member of ε is removed. Then, to repeat the bad part of ε, the j-1'th element of ε is repeatedly inserted to ε, changing what the j-1'th element is. Instead of repeating the bad part my variable number of times, I repeated a single member of the bad part my variable number of times for the same effect but more efficiently. For further explanation of PrSS and likewise, see the following: - https://googology.fandom.com/wiki/Primitive_sequence_number - https://googology.fandom.com/wiki/Beklemishev%27s_worms Please note that my ε is backwards when reading these.
