Conjecture 5 of arXiv 2610.16266 (v1) says T(99) <= 55. These files give 99-vertex graphs with 169 and 120 triangles that avoid diamond and K_{2,3}.

t99_counterexample.json  99 vertex ids of the srg(243,22,1,2) graph (Cayley graph on F_3^5 from the ternary Golay code)
t99_verify.py            rebuilds the graph, checks srg parameters, the subset's triangle count and common-neighbour bounds (needs numpy)
er9.py                   builds the Erdos-Renyi polarity graph ER(9): 91 vertices, 450 edges, 120 triangles (pure Python)

Run: python3 t99_verify.py t99_counterexample.json
     python3 er9.py
Both checkers were written by AI agents. Last updated 2026-10-20.
