What does this equation mean?

A cap set is a subset of the grid \{0,1,2\}^n with one rule: no three distinct points in it are allowed to sum to zero coordinate-wise modulo three. The largest such set in eight dimensions had been 496 points since 1994. In December 2023, a Google DeepMind system called FunSearch reported one with 512 [ 1 ] . DeepMind’s own announcement called it the largest jump in cap set sizes in twenty years [ 3 ] . Both of those claims check out — this article verified the 512-point construction and the ablation data behind it directly against the paper’s own supplementary material, not against the press release alone [ 2 ] . The question this article asks is not whether FunSearch found something real. It did. The question is what “found” means when the thing doing the finding is a loop that mutates one function, checks the result with a counting program, and keeps whatever counts higher — a loop that, by the DeepMind team’s own account, never once represents the cap set problem as a mathematical object at all.