= Solution
Both central <baryons> have <valence quarks> $uds$, <baryon number> $1$, <strangeness> $-1$ and <isospin> projection zero. Their total <isospins> differ:
$$
\boxed{\Sigma^0:\ I=1,\ I_z=0;\qquad
\Lambda^0:\ I=0,\ I_z=0.}
$$
The $ud$ flavor part is symmetric for the <Sigma baryon> and antisymmetric for the <Lambda baryon>. In the usual <ground state> coupling, the associated $ud$ pair has <spin> one for $\Sigma^0$ and <spin> zero for $\Lambda^0$, with the strange <quark> giving total <spin> $1/2$ in both cases. Distinct total <isospin> makes these orthogonal states despite their coincident position in the <weight diagram>.
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