In 2022, DeepMind's AlphaTensor discovered a new state-of-the-art strategy for multiplying two $4 \times 4$ matrices using only 47 multiplications (under a special arithmetic) instead of the original 49. By integrating this method into a standard divide-and-conquer framework, the complexity of multiplying two $n \times n$ matrices is reduced to $O(n^k)$. Compute $k$ based on the above information to get the tightest upper bound.