What was already known
The conjecture asks whether an affine-space zero fibre must be a coordinate hyperplane. Dimension two and restricted higher-dimensional cases were known, while the general ambient-four case remained open.
AI involvement
OpenAI credits its internal model with the September construction. The later stable-coordinate example is a separate model-produced result.
OpenAI authorship and the release's internal-model provenance support model-led mathematical construction, without proving individual-session autonomy.
- Supporting source (github.com) — Target theorem ends with sorry
- Supporting source (github.com) — How the results were produced and verification-stage caveat
Importance
The example disproves the embedding conjecture in its first unresolved ambient dimension.
Limitations
The available Lean target file states the theorem without a completed proof. The later one-stable-coordinate example uses a different polynomial.
Technical verification
The September paper gives an explicit quotient isomorphism and a vanishing-gradient obstruction. The visible Abhyankar–Sathaye and stable-coordinate ComparatorChallenges end in sorry; they are target statements, not checked proofs. No completed human or machine check of the September theorem is documented, so Reported is the evidence default.
Human understanding
No named human explanation of the cusp-based coordinate-ring isomorphism and noncoordinate obstruction is documented. Few is the evidence default.
Correction and publication history
If correct, the example disproves the embedding conjecture in its first unresolved ambient dimension.
Read this published revision