Breaking the Exponential Wall: A DSA+CSI Black-Box Challenge for the NP-Hard Maximum Clique Problem

The Maximum Clique Problem (MCP) is a cornerstone of combinatorial optimization and graph theory. Traditional exact algorithms, such as Branch and Bound, face an insurmountable exponential wall as graph sizes increase. In this paper, we present empirical results from the DSA+CSI (Daopological Structural Annealing + Corrigible Structural Intelligence) framework. On 100-node random graphs, DSA+CSI identifies a maximum clique of size 10 in 55.62 ms, whereas the exact NetworkX solver hits a 5-second wall-clock limit and returns a sub-optimal clique of size 9. More critically, as the graph scales to 500 nodes, where exact solvers suffer from catastrophic exponential explosion, DSA+CSI converges to a near-optimal solution in just 285.97 ms. To maintain the black-box integrity of the framework for unbiased empirical validation, the underlying code remains closed-source. Instead, we issue a Black-Box Challenge: we provide the full datasets, convergence trajectories, and benchmark results, inviting the global research community to replicate or surpass our performance.