I think skipping transposed values is fine though. You could just mirror the output at 45degrees for that if you wanted it. It does hit all distinct triples including the multiples of triples so it’s more inclusive of everything than the ternary tree.

You can see both triples are contained in one binary tree using the big diagram in section 3. The triple [3 4 5] has the "path" RR. The triple [4 3 5] the path R.