What was already known
Every complete local domain of dimension at most two has a small Cohen–Macaulay module; the general domain existence conjecture remained open in higher dimension.
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 domain form of the small Cohen–Macaulay module conjecture in dimension three.
Limitations
The linked Lean scope verifies a candidate ring’s normality, completeness, dimension, and residue field, but not the absence of maximal Cohen–Macaulay modules—the decisive counterexample property remains unchecked there.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
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 Lean-scope mismatch review for non-notifying local inclusion.
Read this published revision