A unified, machine-checkable catalog covering shapes up to 32×32×32 over Q, Z, R, C, F₂ and F₃, plus a separate axis for commutative algorithms (Waksman 1970, Makarov 1986, Rosowski 2019).
Its exhaustive derivation operators — axis-flip, Kronecker, axis concatenation, recombination-with-allocation, and downward projection — are iterated to a fixed point.
Against the best external catalog it improves 908 of the 4,760 comparable shapes (19%, all in the 17–32 band), ties 3,688 more, and trails on only six.