Primariness of the Mixed-Norm Space
A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of as a prominent remaining open case; the paper proves it is primary for .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Banach Space Decomposition Theory
- Posed by
- Lechner, Motakis, Müller and Schlumprecht
- Year posed
- —
- Years open
- —
- 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.
Source
Submitted by Curator34