What was already known
Polynomial mixing was established for special degree sequences; the Kannan–Tetali–Vempala conjecture asked for all graphical degree sequences.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the simple-undirected Kannan–Tetali–Vempala switch-chain conjecture with an explicit polynomial bound.
Limitations
The formalized claim concerns mixing of the specified lazy switch chain. The paper’s separate exact uniform sampling algorithm is outside the pinned Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note identifies switch-chain connectivity and mixing time at most 2n⁸ for every graphical degree sequence.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every graphical degree sequence on n≥4 vertices, the lazy simple-undirected switch chain that proposes switches uniformly on four vertices has total-variation mixing time at distance 1/4 at most 2n⁸.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision