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A Structural Proof of the Lower Bound 21 for $3\times3$ Matrix Multiplication over $\mathbb F_2$
We prove that the tensor rank of $3\times3$ matrix multiplication over $\mathbb F_2$ is at least $21$. The structural proof, independently developed by Qiushi Engine, converts occupation constraints on a single tensor factor into algebraic relations coupling all three factors. Certified quotient-ran
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