LLM-guided search beats 30-year Shannon capacity bounds

Itty, Rosin, Carstensen and Reichman used a language model to raise three 30-year-old Shannon capacity bounds, per a new arXiv paper. That matters for anyone skeptical of AI math claims. The result is a set of numbers a computer can check directly, not a proof that needs a referee's judgment.

The new sets have 134,753 elements in C7^10, 21,909 in C11^6 and 62,530 in C13^6. Those push the bounds to Θ(C7) above 3.258020, Θ(C11) above 5.289773 and Θ(C13) above 6.300109. The researchers found them through iterative interaction with the model, according to the paper.

That's what separates this from most claims about AI doing math. An independent set of a given size either exists or it doesn't, and checking it is mechanical.

No peer review queue, no prose proof to evaluate for gaps. The paper's credibility rests on that property, not on trusting the model's reasoning.

The catch is how narrow that credibility is. It holds because Shannon capacity has a checkable answer, not because the model understands graph theory. Expect more results like this in problems a computer can verify, not ones that hinge on a natural-language proof.

The paper posted to arXiv in July 2026, when a Shannon capacity bound moving on a mechanically checkable proof is still rare enough to notice.