No wonder that you can arbitrarily reduce requirements for negative energy, which means you can drop negative energy to zero. I was suggesting something like that to @Thomas R. Morrison, that one doesn't need negative energy for warp drive. Purely based on common sense. Warp drive has to bubbles, one is pushing one is pulling. Well, everybody knows that you can arrange horses either behind a cart to push it, or in front of cart to pull it. One doesn't need horses both behind and in front of the cart.