On boundedness of singularities and minimal log discrepancies of Kollár components, II

We show that a set of K-semistable log Fano cone singularities is bounded if and only if their local volumes are bounded away from zero, and their minimal log discrepancies of Kollár components are bounded from above. As corollaries, we confirm the boundedness conjecture for K-semistable log Fano cone singularities in dimension three, and show that local volumes of 3-dimensional klt singularities only accumulate at zero.