diff --git a/network_process/interface/fwd_types.hpp b/network_process/interface/fwd_types.hpp
index 94cc6db..ce04a2c 100644
--- a/network_process/interface/fwd_types.hpp
+++ b/network_process/interface/fwd_types.hpp
@@ -227,6 +227,17 @@ struct hash<pod_key_t<N>> {
     size_t operator()(const pod_key_t<N>& k) const { return XXH3_64bits(&k, sizeof(pod_key_t<N>)); }
 };
 
+template <>
+struct hash<compact_bg_mesh_coord_t> {
+    using argument_type = compact_bg_mesh_coord_t;
+    using result_type = size_t;
+
+    result_type operator()(const argument_type& coord) const noexcept {
+        // 使用 uint64_t 的哈希算法，将 hashed_value 映射为 size_t
+        return static_cast<result_type>(std::hash<uint64_t>()(coord.hashed_value));
+    }
+};
+
 template <>
 struct equal_to<vertex_header_t> {
     bool operator()(const vertex_header_t& v1, const vertex_header_t& v2) const