Why does the yield curve slope upward?

Large baskets empty into small baskets.    

With a shift of terms, I can say a house holds our household goods, it is container algebra. Because goods are conserved, we will therefore have fewer large baskets than small baskets.  Please refer to basket brigade theory. Thus, large basket, having fewer of them, will have higher lower liquidity when transferred (higher interest charges). The law of large numbers is sufficient proof.

Why can't the curve invert? Because we would have to go find all the small baskets and make them return their contents to the large baskets. We cannot reverse the expansion of entropy, we cannot find all the small baskets for a claw back, we have to take the losses and move on, a requant.

Time is irrelevant in this process, terms are set via another process called default swaps.  The stated terms are nominal, not real; but close.  We pack sphere.  We are rarely meeting the Euler conditions, so time derivatives won't work. We run a sparse system.

We hear a lot of curve analysis on the basis that everything is time synced, we have complete transaction spectrum, which is the implication of the Euler conditions. The analysis ends up with an indeterminate construction of rates. It is the Magic Walrus problem, which most economists now understand.