What was already known
Earlier work gave a width upper bound of 4 for symmetric polar products, while matching embeddings were known for special bodies.
AI involvement
OpenAI attributes the released manuscript and proof to an internal model. The record does not establish result-specific autonomy.
The internal-model release credits AI with the manuscript and proof, but gives too little interaction detail for autonomy.
Importance
Answers a general symplectic-width question for symmetric polar products.
Limitations
The stated theorem does not assert an embedding at capacity exactly 4. No named human check or explanation of the construction is documented.
Technical verification
The cited Lean formalization reports the width-four statement and c<4 embeddings.
Formal checking
Lean proof term for the selected statement, with source-reported formalization and no AIProofWatch replay
- Checker
- OpenAI Lean formalization
- Scope
- Gromov width 4 for symmetric polar-product interiors, with embeddings for c<4
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central embedding construction is documented; Few is the evidence default.
Correction and publication history
The width-four embedding theorem is assessed separately from companion Mahler inequalities.
Read this published revision