A Unital Banach Algebra That Is Not a Calkin Algebra
resolvedconfidence 70%
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Precise statement
The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.
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fidelity, correctness, priority, or novelty.
What AI did
ChatGPT 5.5 Pro
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.
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.
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Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
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VibeMath has not independently audited the mathematical statement, proof, or novelty claim.