What was already known
Classical Elton–Odell gave ordinary uniform separation. Toroidal separation >1 without a uniform margin and uniform toroidal results under added geometric assumptions were known.
AI involvement
The model found two proofs for Tomasz Kania’s problem. Antonio and Pablo Acuaviva verified and edited the first proof, including the incomplete-space case.
The paper says the Part II proof search was fully model-driven and humans supplied no next lemma or intermediate mathematics; later human verification and editing do not erase that proof-generation autonomy.
Importance
Extends ordinary Elton–Odell separation to a uniform toroidal bound without completeness or extra geometric assumptions.
Limitations
The authors manually verified the first model proof used in the paper. A second released model proof did not receive the same review.
Technical verification
The authors explicitly say the included first proof was manually verified; the unverified second proof is outside this assessment.
Formal checking
Manual review and editing of the included first proof
- Checker
- Antonio and Pablo Acuaviva
- Scope
- Theorem 5.1 uniform toroidal separation for all infinite-dimensional complex normed spaces
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the proof's Banach-space cases and distinguish the checked first proof from the second unverified method.
Correction and publication history
Extends ordinary Elton–Odell separation to a uniform toroidal bound without completeness or extra geometric assumptions.
Read this published revision