A Ternary Rank-150 Decomposition of ⟨5,6,7⟩ over ℤ, in a New Orbit

We report an exact algorithm for the product of a 5×6 by a 6×7 matrix that uses 150 multiplications in which every coefficient is −1, 0 or +1. Rank 150 is the best rank published for ⟨5,6,7⟩ in any coefficient domain; the rank-150 scheme in the public catalogue carries coefficients up to absolute value 12. To the best of our knowledge the scheme presented here is the first ternary decomposition at the record rank for this format over ℤ. Its de Groote profile differs from that of the catalogued scheme, so the two are inequivalent under the sandwiching action of GL5(ℤ)×GL6(ℤ)×GL7(ℤ): this is a decomposition in a new orbit, not a rescaling of a known one. The scheme reconstructs all 44 100 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 re-derives every claim inside an isolated container.