Disproof of the Ibragimov-Iosifescu conjecture for phi-mixing sequences
A Lean development constructs a stationary phi-mixing sequence with finite second moments whose normalized partial sums fail to satisfy the central limit theorem, disproving a 1971 conjecture.
- Model
- GPT-6 Astra (pre-release)
- Field
- Mathematics
- Date
- 2026-09-05
- Human collaborators
- Tom Adamczewski
- Problem posed
- 1971 · open 55 yrs
Sources
Original work
Independent commentary
What was found
Ibragimov conjectured that a strictly stationary phi-mixing sequence with finite second moments and diverging partial-sum variance satisfies the central limit theorem; Iosifescu's stronger form asks for convergence of the rescaled partial-sum process to Brownian motion. The construction uses bounded causal feedback to suppress ordinary fluctuations while rare large spikes retain the variance, giving variance divergence together with collapse of the normalized sums along a subsequence. Disproving Ibragimov's form rules out Iosifescu's, since that convergence would give the central limit theorem at time one. The recorded verification reports the standard three axioms only.
Novelty check
The repository carries its own literature review documenting a search through 2026-09-05 for a prior resolution. It reports finding no earlier counterexample satisfying all the conjecture's hypotheses, and identifies a 2023 scholarly source still describing the conjecture as open. That review was not independently repeated for this entry. No competing claim appears in the four registries.
Caveats and known objections
Unrefereed and days old at entry, with no probabilist on record as having read it. The grade is claimed rather than formal for the usual reason on this pipeline: the axiom check establishes that the Lean proves the recorded statement, not that the recorded statement is the conjecture as the literature states it, and no third party has audited that step. Autonomy is ai-led rather than autonomous, weaker than the sibling Smale entry: the disclosure says the model constructed the counterexample and wrote the proof over roughly twelve hours and 1054 turns, which describes an agentic run rather than the unsteered single attempt the benchmark entries rest on.
Also recorded at
vibemathedibragimov-iosifescu-varphi-mixing-clt-conjecture
Nothing mechanically. It is a parallel listing of the same result, carrying its own verification label rather than an independent check.
Nobody outside the lab has checked this yet.
Reading the primary source closely enough to say whether it supports the claim counts as a check, and you are credited on the entry.
Or on GitHub: submit a check challenge the grade send a correction or send a pull request
Flag this for triage
Signals order the review queue and nothing else. They are never published, and they never move a grade: that takes a citation.
Entry history (1 event)
- AddedEntered the registry graded Claimed and AI-led.
Entries are never deleted. A grade that does not hold up is downgraded on the record, with the reason beside it.
Graded claimed for verification and ai-led for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Disproof of the Ibragimov-Iosifescu conjecture for phi-mixing sequences. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-05-ibragimov-iosifescuBibTeX
@misc{whataifound-openai-2026-iosifescu,
title = {Disproof of the Ibragimov-Iosifescu conjecture for phi-mixing sequences},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by OpenAI / Epoch AI. Verification: Claimed. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-09-05-ibragimov-iosifescu}
}