Matrix multiplication: omega at most 9/4 over every ring
An integral extension of OpenAI's matrix multiplication exponent bound and its previous all-fields extension. The formalization proves that the exact integer coefficient tensor-rank exponent is at most 9/4, yielding division-free arithmetic programs over every associative unital ring, including noncommutative rings. For every positive epsilon, one constant bounds the operation count at all positive matrix sizes by C*n^(9/4+epsilon). The arithmetic model is preserved apart from Field-to-Ring assumptions. The extension uses a primitive tensor spectrum, coefficient extraction, fixed finite-free…
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