What was already known
The stable-coordinate statement was known to hold over the complex numbers in two and three variables, making four the first possible dimension for such a counterexample 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
Refutes the stable-coordinate conjecture at its first possible complex dimension and gives a nonrectifiable affine-three-space embedding.
Limitations
The selected result concerns four variables. It is a distinct polynomial-coordinate statement related to, but not identical with, the fourfold cancellation counterexample.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers the explicit degree-five one-stable polynomial, its failure to be a coordinate, and its nonrectifiable affine-three-space fibers.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- An explicit degree-five polynomial in four complex variables is not a coordinate there but becomes a coordinate after one new variable; each fiber is affine three-space without an ambient rectification.
- 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