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FGG Conjecture for QAOA on the Ring of Disagrees

For an even cycle of size NN and depth pp with 2p+2N2p + 2 \le N, is the optimal QAOA approximation ratio for MaxCut exactly 2p+12p+2\frac{2p+1}{2p+2}, as Farhi, Goldstone and Gutmann conjectured?

Result
Proved
Status
Resolved
AI contribution
AI-discovered
Method
Argument
Field
Quantum optimization
Posed by
Edward Farhi, Jeffrey Goldstone & Sam Gutmann
Year posed
2014
Years open
12y
Solved
2026-06-29
Model
Claude Fable 5
Vendor
Anthropic
Collaborators
Verification
Lean-verified
Publication
Preprint
Significance
15 / 100
Disclosed cost
Wikipedia
No dedicated article

What the AI did

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).

Verification

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

Sources

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

Discussion