Weakly Compact Factorization Through a Space With a Basis
Davis, Figiel, Johnson and Pełczyński showed their interpolation space admits a Schauder basis when the range space has a shrinking one. Can the DFJP space always be chosen with a basis whenever the range space has a basis? The paper proves it can.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Banach Space Factorization
- Posed by
- Davis, Figiel, Johnson and Pełczyński; raised again by Kevin Beanland
- Year posed
- 1974
- Years open
- 52y
- Solved
- 2026-07-19
- Model
- ChatGPT 5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Antonio Acuaviva, Pablo Acuaviva
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
ChatGPT 5.5 Pro, driven directly and through Codex agents over a filesystem, generated the key ideas and the proof; the authors verified and refined it. The paper reports that the model sometimes misattributed a theorem, cited a result imprecisely, or presented steps as immediate when they still needed checking, so the human verification was load-bearing. The authors state none of these results came from the newer generation of models.
Verification
No independent check. The proof stands on verification by the paper's authors, who describe correcting misattributions and filling in steps the model presented as immediate. Preprint, not refereed.
Sources
Submitted by Curator34