What was already known
A fully polynomial randomized approximation scheme was known for bipartite perfect matchings, while the general-graph counting problem remained open in the manuscript’s account.
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 long-standing general-graph perfect-matching approximation problem.
Limitations
The algorithm’s guarantee concerns finite simple undirected graphs and randomized relative approximation. OpenAI reports the Lean check; it was not rerun here.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note specifies an FPRAS for every finite simple undirected graph, including zero output on infeasible instances and worst-case polynomial bit time.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A randomized algorithm approximates the number of perfect matchings in every finite simple undirected graph to relative error ε with failure probability at most δ in worst-case bit time polynomial in the input length, ε⁻¹, and log δ⁻¹; it returns zero with certainty when there is no perfect matching.
- 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