What was already known
Pełczyński had proved the implication under weak compactness and shown it fails without qualification for nonseparable range; Beanland's separable-range question remained open.
AI involvement
The model found the central proof for Kevin Beanland’s question. Antonio and Pablo Acuaviva checked, locally corrected and rewrote it.
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
Settles Beanland’s separable-range question through a weak-star extraction and quotient-factorization argument.
Limitations
The equivalence does not extend to arbitrary nonseparable range.
Technical verification
The two authors report a complete human mathematical check of the printed proof; no machine formalization is claimed.
Formal checking
Human mathematical reading, reference and hypothesis checks, and minor corrections
- Checker
- Antonio and Pablo Acuaviva
- Scope
- Theorem 7.2 equivalence for separable Y
- 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 earlier weak-compactness boundary and the weak-star extraction/quotient factorization that closes the separable case.
Correction and publication history
Settles Beanland’s separable-range question through a weak-star extraction and quotient-factorization argument.
Read this published revision