Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Swinnerton-Dyer (1981) proved $R$-equivalence trivial on smooth cubic surfaces over $p$-adic fields with good reduction, except for three special types. The paper resolves two long-standing exceptional cases: triviality for the diagonal cubic over $\mathbb{Q}_3$, answering a question from Manin's Cubic Forms (1972), and the cubic with universal equivalence of exponent 2 (Kanevsky, 1982).
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
"This is the first in a series of works derived from a year of interactions with generative AI models such as AlphaEvolve and Gemini 3 Deep Think, with the latter proving many of our lemmas." The paper devotes a section to the timeline and nature of the AI use; the authors are career AI researchers at Google DeepMind, and Kanevsky posed one of the resolved cases himself in 1982.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
No verification note supplied.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.