I had a similar experience with regular o1 about integral that was divergent. It was adamant that it wasn't and would respond to any attempt at persuasion with variants of "its a standard integral" with a "subtle cancellation". When I asked for any source for this standard integral it produced references to support its argument that existed but didn't actually contain the integral. When I told it the references didn't have the result and backpedalled (gaslighting!) to "I never told you they were in there". When I pointed out that in fact it did it insisted this was just a "misunderstanding". It only relented when I told it Mathematica agreed the integral was divergent. It still insisted it never said that the books it pointed to contained this (false, non-sensical) result.
This was new behaviour for me to see in an LLM. Usually the problem is these things would just fold when you pushed back. I don't know which is better, but being this confidently wrong (and "lying" when confronted with it) is troubling.