Flood and Harvest: The Provable Necessity of Trivia for Generating Valuable Mathematics via the Lens of Language Generation in the Limit
AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint. We model the generation of valuable mathematics as nested language generation in the limit: a verifiable formal language $F$, accessed through a membership oracle (the proof checker), contains an unknown valuable language $H \in \mathcal{H}$ revealed only through an adversarial enumeration of a core $C \subseteq H$ of exact density $α$ (the literature). Every output is valuable ($\in H$), trivial ($\in F \setminus H$), or a hallucination ($\notin F$). We settle four questions. First, the verif...
| Authors | Xiaoyu Li, Andi Han, Dai Shi et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 June 2026 |
| Last updated at source | 12 June 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.