diff --git a/fano_cartier_sections_v2.txt b/fano_cartier_sections_v2.txt
index 7a44b29..3968319 100644
--- a/fano_cartier_sections_v2.txt
+++ b/fano_cartier_sections_v2.txt
@@ -235,7 +235,7 @@ If v is also centered, with t = 1/2 and v(f) >= (1 + gamma) w(f) > 0 for 0 < gam
 where c(n, gamma) > 0 depends only on n and gamma. Consequently two valuations whose volumes are within relative o(1) of the minimum on the same A = 1 common slice are multiplicatively 1 + o(1) equal on all regular functions, and a sufficiently small fixed relative error gives any prescribed fixed multiplicative closeness to one.
 
 ./pdf/li-minimizing-normalized-volumes-2018.pdf
-./pdf/li-xu-normalized-volume-ineualities-2018.pdf
+./pdf/li-xu-normalized-volume-inequalities-2018.pdf
 
 The gap proof adapts a basis to the w-flag and the v-flag simultaneously. Lifts of a homogeneous complement of a_{gamma N/4}(w), multiplied by f raised to the power floor(N / w(f)), have w-value less than (1 + gamma/4) N and v-value at least (1 + 2 gamma/3) N. These contribute at least
 
@@ -376,7 +376,7 @@ Third clause. The saturation hypothesis demands T_i(s) >= m for every regular se
 Conclusion of the obstruction. No sequence can exist, and the pinning obstruction is proved.
 
 ./pdf/xu-zhuang-stable-degenerations-2025.pdf
-./pdf/li-xu-normalized-volume-ineualities-2018.pdf
+./pdf/li-xu-normalized-volume-inequalities-2018.pdf
 
 Completion of the birational theorem. Combine the reduction to the local model (first paragraph of the proof) with the pinning obstruction. The reduction produces, for any failing sequence of birational klt complement problems, a sequence satisfying all hypotheses of the pinning obstruction. The pinning obstruction excludes all such sequences. Hence no failing sequence exists, and there is a uniform n = n(d, epsilon) for every d and epsilon.