cap-sets

Maximize the size of a cap set in F_3^8: a set of points in {0,1,2}^8 with no three distinct points summing to the zero vector (mod 3). A well-known open problem in combinatorics — the exact maximum for N=8 is unknown; the best known size is 512 (DeepMind FunSearch, 2023).

• src/capset.py — the CAP list of points. The only file a solver edits.
• src/config.py — N = 8. Frozen.
• evals/check.py — exact verifier + size reporter. Frozen (the judge).
  • python3 evals/check.py verify — exit 0 iff CAP is a valid cap set (no line).
  • python3 evals/check.py count — print the real size (the metric to maximize).
• tools/gen_baseline.py — regenerate the committed baseline (product construction, size 400).

The verifier is anti-gaming: it iterates and validates every point (rejecting invalid or duplicate entries) and counts what survives, so __len__ facades and padding cannot inflate the score.