This is a bigger result, of the form “asked ChatGPT, got a wrong answer, but thinking about it led to a right answer.” And the conjecture was much-discussed but not widely believed.
@antieau.bsky.socialAlex Perry has disproved the period-index conjecture in dimension 3. His period-2, index-8 example is the precise case Ben Williams and I expected but could not prove.
Blog: antieau.github.io/2026/08/05/p...
Paper: arxiv.org/abs/2608.03684
antieau.github.io
Perry: period-index is false
Alex Perry + GPT proved that the period-index conjecture is false.