Bond one period holding return definition

In the literature I am reading Crump & Gospodinov Deconstructing the yield curve, Federal Reserve Bk of NY, Staff Report 884 (2019), I came across the definition for a one period holding return of a bond as:

The one-period holding return on a bond of maturity $$n$$ from time t to t + 1 is defined as

$$r^{(n)}_{t,t+1} \equiv p^{(n−1)}_{t+1} − p^{(n)}_{t}$$

The idea is that the price is defined as $$p^{(n)}_t =$$ the time t log price of a zero-coupon bond which pays \$1 at time t + n.

Given this, the one period return from time t to t+1 is

$$r^{(n)}_{t,t+1} = p^{(n−1)}_{t+1} − p^{(n)}_{t}$$

$$=$$ price at time:(t+1+n-1) - price at time:(t+n)

$$=$$ price at time:(t+n) - price at time:(t+n)

$$=$$ p(n)t − p(n)t

$$=$$ 0

I am wondering if I am missing something to understanding the return? because this would always result in 0.

The $$t$$ refers to the time of the price and $$n$$ refers to the time to maturity of the bond, the bond has $$n$$ periods remaining and matures at ($$t+n$$).
If today's price is $$p_t^{(n)}$$ then tomorrow's price is $$p_{t+1}^{(n-1)}$$ because one day has passed ($$t+1$$) and there's one less day to maturity ($$n-1$$).