Remark: Family 139. Subpolynomial queries for log-concave sampling

For $C^2$ potentials with a supplied minimizer and $I⪯{\nabla }^{2}V⪯2I$, proves that sampling within total variation $1/10$ requires only $C_{\epsilon }{d}^{\epsilon }$ exact value-and-gradient queries for every fixed $\epsilon >0$. The bound holds on every run, with unrestricted computation between queries. A logarithmic lower bound also holds, so the optimal power-law exponent in this oracle model is zero.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.