$U$-spin sum rules in charmed baryon decays beyond the $U$-spin limit

$U$-spin symmetry is an important flavor symmetry in studying charmed hadron weak decays. However, the sizeable $U$-spin breaking limits the predictive power of $U$-spin symmetry. In this work, we derive dozens of rate and decay parameter $U$-spin sum rules for charmed baryon decays beyond the exact $U$-spin symmetry limit. These sum rules provide tests of flavor symmetry up to the first-order $U$-spin breaking in the charmed baryon sector.