The Ibragimov-Iosifescu conjecture asks whether a strictly stationary, centered, square-integrable phi-mixing sequence satisfies a
central limit theorem whenever the variance
of its partial sums tends to infinity. Writing 
, the proposed conclusion is convergence
in distribution of 
to the standard
normal distribution. The historical question and precise conventions are documented
in Adamczewski (2026).
Adamczewski (2026) released a candidate counterexample constructed autonomously by GPT-6 Astra. The claimed process meets these hypotheses, but along a subsequence the normalized sums converge in probability to zero. Rare large fluctuations maintain divergent variance even while the normalized sums concentrate near zero along those times.
The Lean proof uses standard logical axioms, but the formal problem statement was itself generated by AI. As of Sep. 7, 2026, neither an independent probabilist's review nor an independent audit matching the formal definitions to the classical conjecture had been reported (VibeMathed 2026).
