diff --git a/include/geode/basic/attribute_manager.hpp b/include/geode/basic/attribute_manager.hpp
index b1da00dc7..60907632c 100644
--- a/include/geode/basic/attribute_manager.hpp
+++ b/include/geode/basic/attribute_manager.hpp
@@ -60,7 +60,7 @@ namespace geode
         [[nodiscard]] std::shared_ptr< AttributeBase > find_generic_attribute(
             std::string_view name ) const
         {
-            absl::ReaderMutexLock lock{ &mutex() };
+            absl::ReaderMutexLock lock{ mutex() };
             return find_attribute_base( name );
         }
 
@@ -74,7 +74,7 @@ namespace geode
         [[nodiscard]] std::shared_ptr< ReadOnlyAttribute< T > > find_attribute(
             std::string_view name ) const
         {
-            absl::ReaderMutexLock lock{ &mutex() };
+            absl::ReaderMutexLock lock{ mutex() };
             auto attribute =
                 std::dynamic_pointer_cast< ReadOnlyAttribute< T > >(
                     find_attribute_base( name ) );
@@ -110,7 +110,7 @@ namespace geode
             AttributeProperties properties )
         {
             {
-                absl::ReaderMutexLock lock{ &mutex() };
+                absl::ReaderMutexLock lock{ mutex() };
                 auto attribute = find_attribute_base( name );
                 auto typed_attribute =
                     std::dynamic_pointer_cast< Attribute< T > >( attribute );
@@ -119,7 +119,7 @@ namespace geode
                     return typed_attribute;
                 }
             }
-            absl::MutexLock lock{ &mutex() };
+            absl::MutexLock lock{ mutex() };
             auto attribute = find_attribute_base( name );
             auto typed_attribute =
                 std::dynamic_pointer_cast< Attribute< T > >( attribute );
diff --git a/include/geode/basic/cached_value.hpp b/include/geode/basic/cached_value.hpp
index 27ce2bf71..4294f1e6f 100644
--- a/include/geode/basic/cached_value.hpp
+++ b/include/geode/basic/cached_value.hpp
@@ -74,7 +74,7 @@ namespace geode
         {
             if( !computed_ )
             {
-                absl::MutexLock lock{ &mutex_ };
+                absl::MutexLock lock{ mutex_ };
                 if( !computed_ )
                 {
                     value_ = computer( std::forward< Args >( args )... );
diff --git a/include/geode/basic/mapping.hpp b/include/geode/basic/mapping.hpp
index fb520cb3b..d4890d593 100644
--- a/include/geode/basic/mapping.hpp
+++ b/include/geode/basic/mapping.hpp
@@ -23,8 +23,9 @@
 
 #pragma once
 
-#include <absl/container/flat_hash_map.h>
+#include <absl/algorithm/container.h>
 #include <absl/container/inlined_vector.h>
+#include <absl/container/linked_hash_map.h>
 
 #include <geode/basic/common.hpp>
 
@@ -71,13 +72,13 @@ namespace geode
             return out2in_.at( out );
         }
 
-        [[nodiscard]] const absl::flat_hash_map< T1, Storage< T2 > >&
+        [[nodiscard]] const absl::linked_hash_map< T1, Storage< T2 > >&
             in2out_map() const
         {
             return in2out_;
         }
 
-        [[nodiscard]] const absl::flat_hash_map< T2, Storage< T1 > >&
+        [[nodiscard]] const absl::linked_hash_map< T2, Storage< T1 > >&
             out2in_map() const
         {
             return out2in_;
@@ -100,19 +101,21 @@ namespace geode
             return static_cast< index_t >( out2in_.size() );
         }
 
-        [[nodiscard]] absl::flat_hash_map< T1, Storage< T2 > >& in2out_mapping()
+        [[nodiscard]] absl::linked_hash_map< T1, Storage< T2 > >&
+            in2out_mapping()
         {
             return in2out_;
         }
 
-        [[nodiscard]] absl::flat_hash_map< T2, Storage< T1 > >& out2in_mapping()
+        [[nodiscard]] absl::linked_hash_map< T2, Storage< T1 > >&
+            out2in_mapping()
         {
             return out2in_;
         }
 
     private:
-        absl::flat_hash_map< T1, Storage< T2 > > in2out_;
-        absl::flat_hash_map< T2, Storage< T1 > > out2in_;
+        absl::linked_hash_map< T1, Storage< T2 > > in2out_;
+        absl::linked_hash_map< T2, Storage< T1 > > out2in_;
     };
 
     template < typename T >
@@ -225,6 +228,10 @@ namespace geode
             }
             auto& out_map = this->out2in_mapping().at( out );
             const auto itr2 = absl::c_find( out_map, in );
+            if( itr2 == out_map.end() )
+            {
+                return;
+            }
             out_map.erase( itr2 );
             if( this->out2in( out ).empty() )
             {
diff --git a/include/geode/model/mixin/core/component_type.hpp b/include/geode/model/mixin/core/component_type.hpp
index 41b99333e..0a27d659b 100644
--- a/include/geode/model/mixin/core/component_type.hpp
+++ b/include/geode/model/mixin/core/component_type.hpp
@@ -84,6 +84,15 @@ namespace geode
             return type_.get() == other.type_.get() && id_ == other.id_;
         }
 
+        [[nodiscard]] bool operator<( const ComponentID& other ) const
+        {
+            if( type_.get() != other.type_.get() )
+            {
+                return type_.get() < other.type_.get();
+            }
+            return id_ < other.id_;
+        }
+
         [[nodiscard]] std::string string() const
         {
             return absl::StrCat( type_.get(), " ", id_.string() );
diff --git a/include/geode/model/mixin/core/detail/components_storage.hpp b/include/geode/model/mixin/core/detail/components_storage.hpp
index e791ef5e8..61f9781ba 100644
--- a/include/geode/model/mixin/core/detail/components_storage.hpp
+++ b/include/geode/model/mixin/core/detail/components_storage.hpp
@@ -27,8 +27,8 @@
 #include <fstream>
 #include <memory>
 
-#include <absl/container/btree_map.h>
 #include <absl/container/flat_hash_map.h>
+#include <absl/container/linked_hash_map.h>
 #include <absl/strings/match.h>
 
 #include <bitsery/ext/std_map.h>
@@ -52,7 +52,7 @@ namespace geode
         {
         public:
             using ComponentPtr = std::unique_ptr< Component >;
-            using ComponentsStore = absl::btree_map< uuid, ComponentPtr >;
+            using ComponentsStore = absl::linked_hash_map< uuid, ComponentPtr >;
             using Iterator = typename ComponentsStore::const_iterator;
 
             [[nodiscard]] index_t nb_components() const
diff --git a/include/geode/model/mixin/core/vertex_identifier.hpp b/include/geode/model/mixin/core/vertex_identifier.hpp
index 5d7e03be3..324408fe9 100644
--- a/include/geode/model/mixin/core/vertex_identifier.hpp
+++ b/include/geode/model/mixin/core/vertex_identifier.hpp
@@ -57,6 +57,8 @@ namespace geode
 
         [[nodiscard]] bool operator==( const ComponentMeshVertex& other ) const;
 
+        [[nodiscard]] bool operator<( const ComponentMeshVertex& other ) const;
+
         template < typename Archive >
         void serialize( Archive& archive );
 
diff --git a/src/geode/basic/CMakeLists.txt b/src/geode/basic/CMakeLists.txt
index 93b50b166..530c02228 100644
--- a/src/geode/basic/CMakeLists.txt
+++ b/src/geode/basic/CMakeLists.txt
@@ -109,6 +109,7 @@ add_geode_library(
         "internal/array_impl.hpp"
     PUBLIC_DEPENDENCIES
         absl::flat_hash_map
+        absl::linked_hash_map
         absl::strings
         absl::stacktrace
         absl::symbolize
diff --git a/src/geode/basic/attribute_manager.cpp b/src/geode/basic/attribute_manager.cpp
index b568cee7e..0989d08b8 100644
--- a/src/geode/basic/attribute_manager.cpp
+++ b/src/geode/basic/attribute_manager.cpp
@@ -163,7 +163,7 @@ namespace geode
 
         void delete_attribute( std::string_view name )
         {
-            absl::MutexLock lock{ &mutex_ };
+            absl::MutexLock lock{ mutex_ };
             const auto attribute_it = attributes_.find( name );
             if( attribute_it != attributes_.end() )
             {
diff --git a/src/geode/mesh/helpers/convert_surface_mesh.cpp b/src/geode/mesh/helpers/convert_surface_mesh.cpp
index 645948cc3..8da322e02 100644
--- a/src/geode/mesh/helpers/convert_surface_mesh.cpp
+++ b/src/geode/mesh/helpers/convert_surface_mesh.cpp
@@ -23,6 +23,8 @@
 
 #include <geode/mesh/helpers/convert_surface_mesh.hpp>
 
+#include <absl/container/flat_hash_map.h>
+
 #include <geode/basic/attribute_manager.hpp>
 #include <geode/basic/logger.hpp>
 
diff --git a/src/geode/mesh/helpers/detail/split_along_solid_facets.cpp b/src/geode/mesh/helpers/detail/split_along_solid_facets.cpp
index e458e109a..bde7de751 100644
--- a/src/geode/mesh/helpers/detail/split_along_solid_facets.cpp
+++ b/src/geode/mesh/helpers/detail/split_along_solid_facets.cpp
@@ -139,7 +139,6 @@ namespace geode
             ElementsMapping duplicate_points( const SolidInfo& solid_info )
             {
                 ElementsMapping vertices_mapping;
-                vertices_mapping.reserve( solid_.nb_vertices() );
                 for( const auto vertex_id : Range{ solid_.nb_vertices() } )
                 {
                     vertices_mapping.map( vertex_id, vertex_id );
diff --git a/src/geode/model/mixin/core/vertex_identifier.cpp b/src/geode/model/mixin/core/vertex_identifier.cpp
index 152ca4282..a698b9e5d 100644
--- a/src/geode/model/mixin/core/vertex_identifier.cpp
+++ b/src/geode/model/mixin/core/vertex_identifier.cpp
@@ -78,6 +78,16 @@ namespace geode
         return component_id == other.component_id && vertex == other.vertex;
     }
 
+    bool ComponentMeshVertex::operator<(
+        const ComponentMeshVertex& other ) const
+    {
+        if( component_id != other.component_id )
+        {
+            return component_id < other.component_id;
+        }
+        return vertex < other.vertex;
+    }
+
     template < typename Archive >
     void ComponentMeshVertex::serialize( Archive& archive )
     {