Sharp Hardness for MAX-3-CUT

Precise statement

Assuming the Unique Games Conjecture, it is NP-hard to approximate MAX-3-CUT better than the Frieze-Jerrum semidefinite program does, and similarly for Quantum MAX-CUT: the sharpness question in the Khot-Kindler-Mossel-O'Donnell line, connected to the Plurality is Stablest problem.

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

ChatGPT 5.6

ChatGPT 5.6 assisted in the preparation of the manuscript, including producing the spectral certificates in Propositions 4.1 and 4.4 and Lemmas 9.3 and A.4 - proof components, not prose.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No verification note supplied.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-31

   arXiv

   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.