The story behind the paper
This paper grew out of a project involving Shitan Xu and the authors BK, YS, NT, and MZ, which explored whether GPT-5.6 Sol could prove the main theorem in this paper. After obtaining an initial proof generated entirely by AI, they invited JZ to join the project and help verify it. The authors subsequently checked and simplified the proof, and then wrote the paper from scratch to highlight its central ideas. ChatGPT was additionally used for language editing. The authors take full responsibility for all claims and arguments presented in the paper.
What was previously known to humans and which new ideas came from AI
The overall strategy of the proof predates the use of generative AI and grew out of earlier work on the moduli continuity method, including the goal of proving the Cartierness of the limiting divisor L. In particular, the idea of analyzing the rational map in Section 3.3 already appeared in [Liu22] and in an early version of [LZ25]. In private communications between JZ and Yuchen Liu dating back to 2023, they believed that the K-stability of cubic fivefolds could be proved along these lines, albeit with substantial additional brute-force computation. At the time, however, the main approach was to slice the fivefolds using the limiting linear series, as in [Liu22].
The new ideas contributed by AI are the Cartierness criterion developed in Section 3.2, which relies on Proposition 3.3(4), and the intersection-theoretic arguments in Sections 3.4.1 and 3.4.2. Although the former does not play a central role in the present paper and could potentially be avoided, it introduces a new perspective that may prove useful in future applications. The latter is used more substantially: it controls the singularities and yields a contradiction through global geometric considerations.
