Researchers developed C-HD, a new deterministic shortest path algorithm for directed graphs with non-negative real weights, achieving O(n + m + m*log(2 + m/(n+1)) + m^(1/3)*n*log(n)) complexity in a certified range. The algorithm outperforms Dijkstra and recent SOTA methods by reducing repeated search work through bounded local searches and careful invariant maintenance, with correctness verified using the Lean formal verification tool.