OpenAI · 131-01 · 2026-09-25 · Theoretical computer science
Polynomial mixing of the switch chain for every graphical degree sequence
preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026
Family 131. Polynomial mixing of graph switches with prescribed degrees.
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
Resolves the simple-undirected Kannan–Tetali–Vempala conjecture: the lazy edge-switch chain mixes in time for every graphical labeled degree sequence. The same degree-constrained graphs can also be sampled exactly uniformly by an almost-surely terminating algorithm with expected polynomial bit running time.
We prove the simple-undirected form of the Kannan–Tetali–Vempala conjecture: the switch chain on simple undirected graphs mixes in polynomial time for every graphical degree sequence. For a lazy chain that proposes switches uniformly on four vertices, the total-variation mixing time at distance 1/4 is at most . We also give an exactly uniform sampler for every graphical labeled degree vector. It uses unbiased random bits, terminates almost surely, and has expected polynomial bit running time.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 131: Rapid mixing of graph switches for every degree sequence. 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.