Oh, I see, it's not a true metric. That's fair enough, though I wonder if the result depends critically on that assumption. (you can pass to equivalence classe

Oh, I see, it's not a true metric. That's fair enough, though I wonder if the result depends critically on that assumption. (you can pass to equivalence classes to recover a true metric, and I didn't see anything obviously incompatible with that in the paper, but I admit I didn't look very deeply)