Twenty Signed Products for a Twelve-State Composition Tensor

We give an explicit integer decomposition of a twelve-state composition tensor into twenty signed rank-one terms. The construction uses five scalar characters, seven products for a two-by-two matrix block, and eight remaining products. A square-zero radical and a nine-dimensional semisimple quotient give the bounds 18 ≤ rank(C) ≤ 20 over the real numbers. The nonnegative rank is 35. For every positive integer q, the nonnegative rank of the q-fold tensor power is exactly 35^q, while the signed rank is at most 20^q. The paper includes the coordinate formulas and exact certificates.