Concise tensors of minimal border rank

We determine defining equations for the set of concise tensors minimal border rank in $${\mathbb {C}}^m{\mathord { \otimes } }{\mathbb {C}}^m$$ when $$m=5$$ and $$1_*$$ -generic $$m=5,6$$ . solve classical problem algebraic complexity theory classifying special case Our proofs utilize two recent developments: 111-equations defined by Buczyńska–Buczyński results Jelisiejew–Šivic on variety commuting matrices. introduce a new invariant tensor, its 111-algebra, exploit it to give strengthening Friedland’s normal form 1-degenerate satisfying Strassen’s equations. use 111-algebra characterize wild classify them {C}}^5{\mathord {C}}^5$$