  We study string corrections to one-loop amplitudes of single-particle
operators ${\cal O}_p$ in $AdS_5 \times S^5$. The tree-level correlators in
supergravity enjoy an accidental 10d conformal symmetry. Consequently, one
observes a partial degeneracy in the spectrum of anomalous dimensions of
double-trace operators and at the same time equality of many different
correlators for different external charges $p_{i=1,2,3,4}$. The one-loop
contribution is expected to lift such bonus properties, and its precise form
can be predicted from tree-level data and consistency with the operator product
expansion. Here we present a closed-form Mellin space formula for $\langle
{\cal O}_{p_1}{\cal O}_{p_2}{\cal O}_{p_3} {\cal O}_{p_4}\rangle$ at order
$(\alpha')^3$, valid for arbitrary external charges $p_{i}$. Our formula makes
explicit the lifting of the bonus degeneracy among different correlators
through a feature we refer to as `sphere splitting'. While tree-level Mellin
amplitudes come with a single crossing symmetric kernel, which defines the pole
structure of the $AdS_5\times S^5$ amplitude, our one-loop amplitude naturally
splits the $S^5$ part into two separate contributions. The amplitude also
exhibits a remarkable consistency with the corresponding flat space IIB
amplitude through the large $p$ limit.
