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We study a pair consisting of a smooth 3-fold defined over an algebraically closed field and a “general” 
${\Bbb R}$-ideal. We show that the minimal log discrepancy (“mld” for short) of every such a pair is computed by a prime divisor obtained by at most two weighted blow-ups. This bound is regarded as a weighted blow-up version of Mustaţă–Nakamura’s conjecture. We also show that if the mld of such a pair is not less than 1, then it is computed by at most one weighted blow-up. As a consequence, ACC of mld holds for such pairs.
A pair (X, D) of a projective variety X and a very ample divisor D on X is called stable (resp. semi-stable, resp. unstable) if the Chow point corresponding to the embedding 
is SL(N + 1)-stable (resp. semi-stable, resp. unstable). The criterion for stability is one of the most important steps in proving the existence of moduli spaces.
