Tightness of heuristic contextuality-degree bounds

Determine whether the upper bounds on contextuality degree produced by the heuristic approach of MSGHK24 are tight for configurations whose exact contextuality degrees cannot be computed by the SAT solver.

Background

The exhaustive computations become infeasible for configurations with roughly a thousand contexts, including $K_6\square K_6$, $L(K_{10})$, and unions of more than three graphs. For these instances, the paper uses a heuristic method to obtain upper bounds on the contextuality degree rather than exact values.

Although the heuristic agrees with the SAT solver on every instance where both methods terminate, the authors explicitly caution that conclusions about larger configurations remain uncertain until it is established whether the heuristic bounds are tight.