Sampling regime
Convex body + membership oracle
Compare theorems by mathematical guarantee, rate, and source — not by raw crawler rows.
Theorem and frontier cases
best upper · Normalized SampleWiki statement
Proximal / In-and-Out with restart
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\mathcal R_q\le\varepsilon\]
Complexity / rate
\[\widetilde O(qd^2\Lambda\log^6(1/\varepsilon))\]
lower unknown · Open problem
General sampling lower bound
Matching lower bound not currently known in the pinned literature trail
Matching result remains open.
upper · Normalized SampleWiki statement
Rényi-preserving annealing
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\mathcal R_q\le\varepsilon\]
Complexity / rate
\[\widetilde O(qd^2R^{3/2}\Lambda^{1/4}+qd^2\Lambda\log^7(1/\varepsilon))\]
upper · Normalized SampleWiki statement
Constrained proximal sampler
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\mathcal R_\infty\le\varepsilon\]
Complexity / rate
\[\widetilde O(d^3\,\operatorname{polylog}(1/\varepsilon))\]