What was already known
The 2-to-1 Games Conjecture with perfect completeness had remained open; prior hardness reductions did not establish this full value gap from satisfiable instances.
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
Settles the perfect-completeness 2-to-1 Games Conjecture, a central constraint-satisfaction hardness question.
Limitations
The statement uses a fixed rational soundness parameter and a fixed alphabet for that parameter. 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 covers a deterministic polynomial-time reduction from binary 3SAT to nonempty unweighted 2-to-1 games with the stated completeness and soundness.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every fixed rational 0<δ<1, it is NP-hard to distinguish satisfiable 2-to-1 games from unweighted games of value at most δ, with an alphabet depending only on δ.
- 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