A counterexample to the stable forking conjecture

James Freitag, Scott Mutchnik

Freitag and Mutchnik give a stable theory of an infinite-dimensional vector space over the division ring of fractions of the quantum graph algebra of the random graph, refuting stable forking.

Sources for this record

What was already known

Hart, Kim and Pillay proposed stable forking in 1996. Several special positive cases were known; the general conjecture remained open.

AI involvement AI-centered

Freitag and Mutchnik describe giving GPT-5.6 Sol detailed constraints and a Kim–Pillay strategy; the model supplied the candidate counterexample. The human authors proved the needed facts and wrote the paper.

GPT-5.6 Sol supplied the candidate after detailed human prompts specifying constraints and the Kim-Pillay independence strategy. The authors developed the setup and proofs.

Importance Notable

A counterexample settles the general stable-forking conjecture in the negative.

Limitations

The authors supply a mathematical proof, but the source does not document a separate formal check or outside proof audit.

Technical verification Formal (human)

The authors wrote the proofs establishing the candidate counterexample. This validates the model-supplied candidate rather than checking a separate AI-written proof.

Human understanding Full

The authors explain the construction, independence relation and obstruction to stable forking.

Correction and publication history