VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
How dense can a sum-free subset of the lattice cube $\{1,\dots,n\}^d$ be? Aydinian and Cameron asked for the limiting density, which is also Problem 6 in Ben Green's list of 100 open problems. The natural conjecture is that the optimum is a slice $\{x : 1 \le L(x) < 2\}$ for a linear map $L$, previously known only for $d \le 4$. Proved for all $d$. The paper also shows the same phenomenon fails if the cube is replaced by an arbitrary convex set avoiding the origin.
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.
What AI did
ChatGPT 5.4
One line in the acknowledgements, scoped to one theorem: ChatGPT-5.4 provided the main ideas used in the proof of Theorem 1.5, and helped generate the code for numerically verifying a lemma at small parameters. That theorem is not incidental. The authors call it the main contribution of the paper: a general joint mixability statement in the discrete setting which implies the coupling conjecture that Lepsveridze and Sun had reduced the problem to, and which is what carries the density result to all dimensions.
arXiv preprint, not peer-reviewed. One lemma is verified numerically for small parameters in an appendix; the rest is a linear programming duality argument.
arXiv:2605.00816 - On the largest sum-free subset of the lattice cube
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.