Problem detail · source-aware
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Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general monotone variational inequalities could be improved was open. A large-step inexact Halpern iteration achieves O(T^-2), and O(T^-p) at pth order.
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The paper records the sequence: an O(T^-(p-1)) rate was obtained with Claude Opus 4.6, and on verifying it the authors conjectured a better O(T^-p) result, for which Xinliang Zhang then found a proof with GPT-5.6 Sol. The results were subsequently verified by the human authors, who also link the model's initial proof as a public ChatGPT transcript.
Provider: Anthropic, OpenAI · Prompt public: unknown · Independence: unknown
A preprint days old. The initial AI proof is published as a shareable transcript, which is unusual and welcome, but it is a record of provenance rather than a check by anyone independent.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Improves every prior result for p >= 2 and matches the classical extragradient method at p = 1.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.