Quote by mathwonk

The components of tensors are in italics.
The fact that they are not bold, leads to the confusion that this expression denotes a 0  tensor instead of a 2  tensor,

That expression
is a tensor of rank 0. If you notice, it is the contraction of a second rank covariant tensor with two rank 1 tensors. Such a contraction is always a tensor of rank zero. Why do you keep calling the interval a dstensor?
i.e. equation (1) is a sum of, scalar multiples of, pairwise products of, basic 1 tensors,
hence it is a homogeneous "polynomial" of degree 2 in the basic 1 tensors,
i.e. a 2tensor.
Does that seem believable?

Nope. Sorry.
Pete