  Hyperuniformity is an emergent property, whereby the structure factor of the
density $n$ scales as $S(q) \sim q^\alpha$, with $\alpha>0$. We show that for
the conserved directed percolation (CDP) class, to which the Manna model
belongs, there is an exact mapping between the density $n$ in CDP, and the
interface position $u$ at depinning, $n(x)=n_0+\nabla^2 u(x)$, where $n_0$ is
the conserved particle density. As a consequence, the hyperuniformity exponent
equals $\alpha={4-d-2\zeta}$, with $\zeta$ the roughness exponent at depinning,
and $d$ the dimension. In $d=1$, $\alpha=1/2$, while $0.6> \alpha\ge0$ for
other $d$. Our results fit well simulations in the literature, except in $d=1$,
where we perform our own to confirm this result. Such an exact relation between
two seemingly different fields is surprising, and paves new paths to think
about hyperuniformity and depinning. As corollaries, we get results of
unprecedented precision in all dimensions, exact in $d=1$. This corrects
earlier work on hyperuniformity in CDP.
