yes. I am sure.
first, the third link you've pointed reads:
Thus—formally—hash tables often run in time O(log n).
next, if the question is "is it possible to create an algorithm that, given arbitrary strings of finite length, make associative store/lookup for O(1)"  then the answer is "yes" but these are nonrealistic algorithms.
but  back to reality  reallife alhorithms are O(log N) in best case, but I afraid Perl's one is worse than that and  yet  have you ever heard of socalled "hash complexity attack" that was securityfixed by seed randomization in 5.8.0? To inform you, pre5.8.0 were looking like O(1) but actually were O(n) (or maybe even worse in worst case scenario)
next, your "stackoverflow.com" link contains simply wrong information. IOW, I do not see any proof there that convinces me.
And  your last link does not even mention hashes.
Bother explain what is doing here? TIA!
and finally, do you see something strange in your phrase hash operations are O(1) operations, where 'n' is the number of elements in the hash
?
I could be a bit joking, but I do not trust phrases like that.
you're explaining parameter 'n' that is not presents in your formulae  what other mistakes/typos have you made?
:)
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