AI 中文总结
本文提出一种秩23的3×3矩阵乘法算法，在交替基下用51次加法，加上转换共56次，结合线性规划与稀疏基搜索，并给出机器可验证的证书。
AI 中文摘要
我们给出了一种秩为23的$3\ imes3$矩阵乘法算法，该算法在交替基中使用51次加法和减法。输入和输出转换需要额外的5次加法，因此在普通坐标下总共需要56次加法。该构造结合了线性规划约简与对稀疏基变换的搜索，所得程序以机器可检查的证书形式分发。我们通过精确的系数展开验证正确性，并将核成本与完整乘法的成本区分开来。
英文摘要
We give a rank-23 algorithm for $3\times3$ matrix multiplication using 51 additions and subtractions in alternative bases. The input and output conversions require five further additions, giving 56 additions in ordinary coordinates. The construction combines linear-program reduction with a search over sparse basis changes, and the resulting programs are distributed as a machine-checkable certificate. We verify correctness by exact coefficient expansion and distinguish the kernel cost from the cost of a complete multiplication.
Comments7 pages. Certificate and verification code: https://github.com/Joshua-Stapleton/51-addition-alt-basis-3x3-rank23
