Breakthrough Tracker record
A preprint gives a counterexample to the stable forking conjecture
James Freitag and Scott Mutchnik construct a simple theory whose forking is not always witnessed by a stable formula, contradicting the stable forking conjecture posed by Hart, Kim and Pillay in 1996.
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- Stable ID
math-stable-forking-conjecture-counterexample-2026- Revision
math-stable-forking-conjecture-counterexample-2026.v1- Field
- Mathematics · Model theory and mathematical logic
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Provisional claimed counterexample
- Last checked
AI role
The authors describe the result as AI-generated: guided prompts to GPT-5.6 Sol produced the counterexample and supporting proof route. The authors wrote and checked the final arguments and accept responsibility for them.
Record details
- Problem or result
- The 1996 stable forking conjecture in simple theories
- Authors
- James Freitag and Scott Mutchnik
- Institutions
- University of Illinois Chicago
- Result date
- First-version preprint submitted August 31, 2026
Why it matters
Stable forking is a prominent proposed bridge between stable and simple model theory. A valid counterexample would settle the general conjecture negatively and sharpen the boundary between the two.
Limits
This is a 21-page, non-peer-reviewed preprint. No independent specialist assessment, formal proof or separate construction was located, so the negative resolution remains provisional.
Sources
Correction and revision history
- 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.
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