"Allowed" is probably covering too wide a meaning in your description. Just because something is capable of defining infinite consumption does not mean it was allowed to do so in the proof.
Re:`find` + `mkdir` is Turing complete
by upwardbound on Thursday August 01, 2024 @12:41PM
(#41130989)
The initial state of a Turing Machine tape is that beyond the finite-length input, all of the rest of the infinite tape is blank.
https://en.wikipedia.org/wiki/Turing_machine#:~:text=Cells%2...
Whereas the Rule 110 Cyclic Tags engine requires the infinite tape to contain infinite repetitions of structured patterns, even in order to simply run "while(true)". That's a key difference.
I also agree with zamadatix's sibling comment.
Oh, I see what you mean. That sounds quite easy to work around, actually. Due to the speed of light, only a section containing the disruptions to the repeated pattern need be considered for the initial state; and then you can compute outward from that.
To be fair I've never been 100% sold on the Turing-completeness of rule 110, but your argument isn't landing with me either.