the aop conjecture has been proved completely in a number of special cases. lickteig showed already in 1985 that formula_55, provided that formula_56. in 2011, a major breakthrough was established by catalisano, geramita, and gimigliano who proved that the expected dimension of the set of rank formula_57 tensors of format formula_58 is the expected one except for rank 3 tensors in the 4 factor case, yet the expected rank in that case is still 4. as a consequence, formula_59 for all binary tensors.