Python version: gist.github.com/alex1770/528...

You then get a recursion p -> 1-(1-p^2)^2. If p starts off less than ϕ=(sqrt(5)-1)/2, then p will tend to 0 and if it starts off greater than ϕ then it will tend to 1. (Imagine doing a staircase between the green and purple lines.)

Surprisingly, it actually gave way in the end (or maybe its previous beliefs slipped out of its context window). Curious to know why it latched on to its belief in the first place though.

So for a change, here's an example of the complete opposite with some crazy gaslighting (full transcript in the link):
chatgpt.com/share/675a1a.... I was interested in figuring out why it believed what it did, but couldn't nail it down. Spoiler -->