What was already known
Rapid mixing was known for restricted margin classes; the unrestricted fixed-margin bipartite case of the Kannan–Tetali–Vempala conjecture remained open.
AI involvement
The authors credit ChatGPT 5.5 Pro with the comparison strategy, three-row reduction, harmonic decomposition and initial proofs. They posed and directed the problem, evaluated the arguments and rewrote the paper.
The model is credited with the full mathematical strategy and initial lemmas, while the author directed and rewrote the work.
- Supporting source (arxiv.org) — Later general Mihail–Vazirani counterexample, Related work
Importance
Gives a uniform polynomial mixing bound for all feasible fixed-margin binary matrices.
Limitations
The result is for bipartite binary matrices, not arbitrary undirected degree-sequence graphs. The Lean repository identifies the theorem and build instructions but provides no independent build log.
Technical verification
The paper reports full Lean formalization of its main theorem, and the repository identifies the paper-facing spectral-gap theorem and build instructions. The reviewed repository README describes an intended sorry-free build but provides no independent build log; Formal records the source-reported formalization, without claiming AIProofWatch reproduced it.
Formal checking
The paper and repository report a Lean proof of the fixed-margin spectral-gap bound.
- Checker
- Lean formalization maintained by the paper author
- Scope
- Paper-facing fixed-margin lazy swap-chain spectral-gap bound
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human author evaluated and rewrote the proof, and the paper explains the heat-bath comparison, three-row reduction and harmonic decomposition.
Correction and publication history
The spectral-gap bound covers every feasible binary margin pair.
Read this published revision