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  "problem_id": "vibemathed:sum-free-lattice-cube-density",
  "title": "The Largest Sum-Free Subset of the Lattice Cube",
  "canonical_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.",
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      "title": "arXiv:2605.00816 - On the largest sum-free subset of the lattice cube",
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