diff --git a/.translate/state/laffer_adaptive.md.yml b/.translate/state/laffer_adaptive.md.yml
index 8e8da147..f42b3cd2 100644
--- a/.translate/state/laffer_adaptive.md.yml
+++ b/.translate/state/laffer_adaptive.md.yml
@@ -1,6 +1,6 @@
-source-sha: ae928c862f11a4eed88b03f94e6b4cdb733d855e
-synced-at: "2026-07-18"
+source-sha: 49f31821d3a72024ab5a04ba074b30ad50b2238a
+synced-at: "2026-07-19"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 9
-tool-version: 0.17.0
+tool-version: 0.18.0
diff --git a/lectures/laffer_adaptive.md b/lectures/laffer_adaptive.md
index 48d119b7..e36abf13 100644
--- a/lectures/laffer_adaptive.md
+++ b/lectures/laffer_adaptive.md
@@ -175,8 +175,6 @@ import numpy as np
 import matplotlib.pyplot as plt
 import matplotlib as mpl
 from matplotlib.ticker import MaxNLocator
-from matplotlib.cm import get_cmap
-from matplotlib.colors import to_rgba
 import matplotlib
 from scipy.optimize import root, fsolve
 
@@ -572,4 +570,4 @@ $\pi_t$ 是缓慢地向稳态爬行，而不是迅速跳跃到那里。
 并在短短几期内将 $\pi_t$ 拉向 $\pi_l$。
 
 ```{solution-end}
-```
\ No newline at end of file
+```