Problem detail · source-aware
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For a continuous bounded-variation path with signature $g$, logarithmic signature $l$ and increment $v$, the modified Lyons–Sidorova conjecture predicts the structure of $g$ when $R(l)=\infty$. The paper proves it: $g=1$ when $v=0$, and otherwise a prefix $\alpha$ of the centred path gives $S(\gamma) = S(\alpha)e^{v}S(\alpha)^{-1}$.
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The author reports using ChatGPT for mathematical exploration, critical examination of arguments, testing of intermediate proof strategies, and drafting and editing, and states she reviewed and revised all AI-assisted material and takes full responsibility. The model is not credited with producing the proof.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
No independent check, and the disclosure places the model in a supporting role rather than crediting it with the argument. Preprint, not refereed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.