> (Note: I asked AI for the integral of the Gaussian, I hope it got it right!)

It seems like malpractice to not even check this.

It's an illustration for a blog post on a largely different subject, it really doesn't matter.

Who would be looking up the integral of one of the most common functions in applied math in a random philosophical article aimed mostly at SREs?

I don’t think the word applies to a blog post which its self-described as “ramblings”. The formula’s there to look scary and illustrate a point, nobody’s using it to integrate a Gaussian.