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A 55-Addition Rank-23 Scheme for $3\times3$ Matrix Multiplication via Exact Two-Sided Minimization
We give a scheme that multiplies two $3\times3$ matrices with 23 multiplications and 55 additions over any ring, one addition below the previous record of 56 (Sun, 2026) and the first below 56 for exact non-commutative $3\times3$ multiplication without a change of basis. The scheme forms 13 signed c
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