A Counterexample to the Stable Forking Conjecture

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 31, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: A Counterexample to the Stable Forking Conjecture · Stable Forking Conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

GPT 5.6 Sol
model · ai model contributor · OpenAI

James Freitag; Scott Mutchnik
human · human collaborator

Lineage and corrections

VibeMathed record: A Counterexample to the Stable Forking Conjecture evidence for this event

A Counterexample to the Stable Forking Conjecture parent of this event

A Counterexample to the Stable Forking Conjecture evidence for this event

The paper constructs a simple theory in which forking cannot always be witnessed by a stable formula. Precisely, what fails is: in a simple theory, if $a \not\downarrow_C b$ then there is $\varphi(x,\bar b) \in \mathrm{tp}(a/Cb)$ forking over $C$ whose parameter-free form $\varphi(x,y)$ is stable. The counterexample is an infinite-dimensional vector space over the division ring of fractions of the quantum graph algebra of the random graph. Forking is characterised by an abstract independence relation, and the random graph is encoded into that relation so that it has the order property; stable formulas therefore cannot determine all forking in simple theories. parent of this event

This event attributed to James Freitag; Scott Mutchnik

This event attributed to GPT 5.6 Sol

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