As to your actual question:
However, $1, set to '1' by the last successful match at the lowest-but-one level of recursion, is propagated upward unchanged through several levels of subroutine 'blocks'
I see no evidence for that. After $1 is set to '1', exactly one more recursive call happens, and there it is printed out. Then the recursion ends, and you don't print $1 anymore.
I don't print $1, but it must be '1' at all higher recursion levels because only that value will result in a sum total of 4.
However, I have not had (and will not immediately have) a chance to ponder your link and other responses.
I suppose my chief confusion stems from the fact that $1 starts out undefined, takes on a bunch of other values, then winds up as it started. If it had finished up as '1', my mind would rest a bit easier, but at some point, and only one point mind you, it's leaving some kind of scope and being restored to the value it had upon entry. I could understand all scopes, I could understand none, but I can't (yet) understand just one!
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