White's conjecture (White 1980) asserts that any two multisets of matroid bases having the same multiset union can be connected by symmetric basis exchanges. Larson (2026) gave a counterexample consisting of a binary matroid of matroid rank 9 on 18 elements. GPT-5.5 Pro found the example, and Larson supplied a proof not requiring a computer.
The weaker version allowing arbitrary replacements of two matroid bases by two others with the same multiset union remains open. Thus the counterexample does not refute every version of White's conjecture.
