OpenAI · 115-01 · 2026-09-24 · Theoretical computer science
Exact Uniform Sampling of Contingency Tables with Arbitrary Margins
preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026
Family 115. Sampling and counting contingency tables with arbitrary margins.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For nonnegative integer matrices with prescribed row and column sums, gives exact uniform sampling in expected polynomial bit time and almost-uniform sampling in worst-case polynomial bit time. The dimensions and binary-encoded margins are unrestricted. Also gives a fully polynomial randomized approximation scheme for counting such tables with arbitrary individual cell bounds, including structural zeros, with polynomial cost on every execution.
We give an exact uniform sampler for nonnegative integer contingency tables with arbitrary prescribed margins. It terminates almost surely and has expected bit complexity polynomial in both dimensions and the binary length of the margins. No positivity, balance, sparsity, or fixed-dimension assumption is required.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 115: Sampling and counting contingency tables with arbitrary margins. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.