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Precise statement
On page 408 of Calabi's 1958 paper "Construction and Properties of Some 6-Dimensional Almost Complex Manifolds" we find:
"...it is still unknown whether the sphere $S^6$ or any product manifold $V^2 \times S^4$ ($V^2 = $ any closed, orientable surface) admit any complex analytic structure."
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What AI did
ChatGPT 5.6 Sol
The human authors write the following:
"Statement on the use of AI. At first, GPT 5.6 Sol used the fibration method similar to [7] to construct a complex manifold $X$ fibreed over $P^1$ and claimed that it is homeomorphic to $S^2 \times S^4$. However, the proof provided by GPT 5.6 Sol is cumbersome, incomplete, and misses an essential lemma. Then by comparing the singular fibre of $X$ with the singular fibres of $X_{sph}$, we discovered that that $X$ is likely to be obtained by the blowup-quotient-flop process introduced in this paper, which led to the main theorem 1.2 of this article. Wall’s classification result is also introduced to the authors by GPT 5.6 Sol.
The proofs of lemma 2.3, lemma 3.1, proposition 4.6 are first generated by GPT 5.6 Sol, but it is checked and rewrote by the authors.
This article is also polished by GPT 5.6 Sol on grammars, language, notations, conventions, and some graphs."