  We derive exact expressions for a number of aging functions that are scaling
limits of non-equilibrium correlations, R(tw,tw+t) as tw --> infinity with t/tw
--> theta, in the 1D homogenous q-state Potts model for all q with T=0 dynamics
following a quench from infinite temperature. One such quantity is (the
two-point, two-time correlation function) <sigma(0,tw) sigma(n,tw+t)> when
n/sqrt(tw) --> z. Exact, closed-form expressions are also obtained when one or
more interludes of infinite temperature dynamics occur. Our derivations express
the scaling limit via coalescing Brownian paths and a ``Brownian space-time
spanning tree,'' which also yields other aging functions, such as the
persistence probability of no spin flip at 0 between tw and tw+t.
