The mixed fibre

In a fibre of multiplicities $(3,2)$, let $\Gamma$ be the strict transform of the plane line joining the two cluster supports. Theorem 96.4 reduces any possible nonpositive-beta divisor to a closed point of $\Gamma$ other than its $A_2$ endpoint. The fibre flag has $$S(W^T;\Gamma)=\frac{83}{80}>1,$$ so it does not provide the required estimate. We first treat the $A_1$ endpoint. We then extract the curve with transverse weights $(1,2)$, obtaining semistability over its interior. Finally, an ordinary point extraction improves the interior estimate to $32/29$.