Two leading AI labs have announced that their internal models separately debunked the Exponential Time Hypothesis (ETH), a foundational computer science principle that for decades defined the limits of algorithmic efficiency. While the discovery does not pose an immediate threat to current encryption standards, it introduces uncertainty regarding other security assumptions used to protect internet traffic, potentially impacting how computational difficulty is measured for securing data.
Anthropic reports that its lainternal Claude research model found the key algorithm for a subexponential 3-SAT solution on Oct 16 using 14M output tokens and no human input. The company later formalized the finding across 1,050 Lean modules, though it noted that the full formalization has not yet been checked by a human. The company also claimed its Claude Opus 5.5 model can rederive the refutation from a short technical sketch, as OpenAI similarly claimed its own models had reached the same conclusion shortly before.