OpenAI claims a general-purpose reasoning model found a counterexample to Erdos's unit-distance bound [D]

OpenAI posted a math result today claiming that one of its general-purpose reasoning models found a construction disproving the conjectured n\^{1+O(1/log log n)} upper bound in Erdős’s planar unit-distance problem. Announcement: [https://openai.com/index/model-disproves-discrete-geometry-conjecture/](https://openai.com/index/model-disproves-discrete-geometry-conjecture/) Proof PDF: [https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf](https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf) Abridged reasoning writeup: [https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf](https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf) The mathematical claim, as I understand it, is that there are finite planar point sets with more than n\^{1+δ} unit distances for some fixed δ > 0 and infinitely many n. That would rule out the expected near-linear upper bound, though it does not determine the true asymptotic growth rate. What seems especially relevant for this subreddit is the process claim: OpenAI says the solution was produced by a general-purpose reasoning model, then checked by an AI grading pipeline and reviewed/reworked by mathematicians. The proof PDF also includes the original prompt given to the model, but not the full experimental details: no model name, sampling setup, number of attempts, compute budget, hidden system prompt