What does this equation mean?

Here is where a structural audit earns its keep instead of restating the press release, because the announcement’s own supporting table contains the seed of the correction. DeepMind’s paper states that for three of its results — including the 4×4 case — “the algorithms discovered by AlphaEvolve use complex-valued multiplications which can be used for exact multiplication of complex or real-valued matrices” [ 2 ] . That sentence is true and also incomplete in a way that matters enormously for anyone trying to actually use the result. A complex-valued multiplication is not one hardware operation; multiplying two complex numbers (a+bi)(c+di) by the direct method costs four real multiplications, or three using the classic Gauss/Karatsuba trick — so an algorithm that needs 48 complex multiplications to multiply two real-valued 4×4 matrices is not, in a real-arithmetic implementation, a 48-multiplication algorithm at all. It is a 48-times-some-multiplier-between-three-and-four algorithm, comfortably worse than Strassen’s plain 49 real multiplications for real inputs. The headline number and the number a CPU would actually execute for ordinary real-valued data were, on publication, two different quantities.