Proposed in 1995, it asks whether the best flat cut through a broad class of high-dimensional probability distributions is nearly as effective as the best cut of any shape, differing by no more than a universal constant regardless of the number of dimensions.
The authors worked with AI agents in a process directed by humans, and they say multiple independent researchers have validated the result and identified its central criterion as the key breakthrough, followed by machine-checked formal verification.
According to the authors, it removes a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing, and it shows that the obstacles to navigating high-dimensional spaces do not grow without bound as dimensions increase.
Many results that previously assumed the conjecture can now be stated unconditionally, giving convex geometry, probability, and theoretical computer science a firmer foundation.
The researchers say they explored more than 100 candidate approaches with AI agents, with a researcher reviewing intermediate results, discarding weak directions, and passing promising ones to the next round. This produced a new mathematical criterion that could be applied recursively, with each improved bound feeding a tighter one. An October 1, 2026 version of the paper reduced the dependence on dimension to an extremely slow-growing function, and repeating the whole refinement, with accumulated errors shown to stay bounded, completed the proof in the October 4, 2026 version. In a separate effort, repeated unguided attempts by several leading AI models using roughly the same token budget fell short. The authors have shortened the proof, verified it in the Lean proof-checking system, and plan to release both after final review.