What was already known
Cohomological and geometric dimensions were known to agree above dimension two and in dimension one. The remaining Eilenberg–Ganea conjecture predicted agreement at cohomological dimension two.
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
Disproves the long-standing Eilenberg–Ganea conjecture with a finitely generated residually finite example.
Limitations
The claim concerns ordinary integral cohomological dimension and classifying-space dimension.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs a finitely generated residually finite group with cohomological dimension two and geometric dimension three.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There is a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three.
- 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