A Ternary Rank-154 Decomposition of ⟨2,9,11⟩ over ℤ in a New Orbit, Removing the ±5 Coefficient Range of a 1971 Bound

We report an exact algorithm for the product of a 2×9 by a 9×11 matrix using 154 multiplications in which every coefficient is −1, 0 or +1. Rank 154 is the best rank published for ⟨2,9,11⟩ in any coefficient domain, and it has stood since 1971; the rank-154 scheme in the public catalogue carries coefficients up to absolute value 5. To the best of our knowledge this is the first ternary decomposition at the record rank for this format over ℤ. Its de Groote profile differs from that of the catalogued solution, so the scheme lies in a new orbit of the sandwiching action of GL₂(ℤ)×GL₉(ℤ)×GL₁₁(ℤ) rather than being a rescaling of the known one. We make no claim of structural narrowing here: both schemes are assembled from nine types of rank-one atom, and the difference between the profiles is a redistribution of weight, not a reduction in variety. The scheme reconstructs all 39204 entries of the matrix-multiplication tensor with zero residual over the integers and multiplies integer matrices correctly under direct evaluation. The coefficient archive is committed by SHA-256 in the paper, and a live verification endpoint at https://verify.n-base.io/verify11 re-derives every claim inside an isolated container and signs the transcript with Ed25519.