FGG Conjecture for QAOA on the Ring of Disagrees

Precise statement

For an even cycle of size $N$ and depth $p$ with $2p + 2 \le N$, is the optimal QAOA approximation ratio for MaxCut exactly $\frac{2p+1}{2p+2}$, as Farhi, Goldstone and Gutmann conjectured?

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

Claude Fable 5

Claude Fable 5 found a dynamical-symmetry and quantum-signal-processing argument; the complete proof is checked by the Lean 4 kernel. An independent group proved the same result simultaneously via Laurent-polynomial optimization (arXiv:2606.29562).

Provider: Anthropic · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Machine-verified end to end in Lean 4, with an independent simultaneous human proof of the same theorem.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-06-29

   arXiv:2606.29687 - A machine-verified proof of a quantum-optimization conjecture

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.