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.
← Back to the filtered Breakthrough Tracker
- Stable ID
math-stable-forking-conjecture-counterexample-2026- Revision
math-stable-forking-conjecture-counterexample-2026.v2- Field
- Mathematics · Model theory and mathematical logic
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Revised 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 submitted August 31; substantially revised October 19, 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 remains a non-peer-reviewed preprint without an independent specialist correctness assessment, formal proof or separate construction. Version 2 corrects an algebraic sign in the Ore-condition argument, expands the manuscript from 21 to 26 pages and adds a claimed negative answer to Ziegler's one-variable reduction question without changing the headline counterexample.
Sources
Correction and revision history
- 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.
- 2026-10-22 — Recorded arXiv version 2's corrected Ore-condition sign, expanded motivation and additional Ziegler-question result; retained provisional status because no independent mathematical validation was located.
Machine-readable: JSON v1 · CSV v1 · Schema v1
This individual record remains noindex until a story-specific featured image passes Kingy’s rendered-pixel visual review. The source-linked tracker hub remains the public index.