For an ideal spring mass system, $$(\Delta U_x - \Delta U_{\frac{x}{n}})- \Delta U_{x-\frac{x}{n}}=2(n-1)\Delta U_{\frac{x}{n}}$$

$$n!=\prod\limits_{r=0}^k \Bigl(n-(k-r)\Bigr)\prod\limits_{c=1}^{n-(k+1)} \Bigl(n-(k+c)\Bigr)$$

$$\forall n,k \in \mathbb N, 0<k<n$$

I don't know for sure but I speculate that diffeomorphism can beautifully make any volume contain entirely any physically real object and thus creating tiny amazing pockets throughout the universe.