A Counterexample in Combinatorics: Falsification of a Computational Conjecture

We report the falsification of the following conjecture: Conjecture: For n=6, the maximum size of a cap set in F_3^6 is exactly 112, and this maximum is uniquely achieved (up to affine equivalence) by the set of vectors with weight congruent to 1 modulo 3 in the specific coordinate subspace defined by the . A counterexample was discovered computationally: witness = No verified data for n=8. This result was obtained by the SOVEREIGN autonomous research system.