diff --git a/PROGRESS.md b/PROGRESS.md
index f804c37..912b3af 100644
--- a/PROGRESS.md
+++ b/PROGRESS.md
@@ -382,7 +382,7 @@ vcpkg's imgui 1.91.9 removed the `sdl2-binding` feature (only `sdl3-binding` exi
 
 ## What's Next
 
-Sprint 5 in progress. Step 138 (type-aware code generation) done. Next: Step 139 (library compatibility matrix).
+Sprint 5 in progress. Step 139 (library compatibility matrix) done. Next: Step 140 (constructive coding tests).
 
 ---
 
@@ -484,5 +484,6 @@ Sprint 5 in progress. Step 138 (type-aware code generation) done. Next: Step 139
 | 2026-02-09 | Codex | Step 136: Agent preferImports/strictMode policy checks on mutations with warnings or blocking. 4/4 tests pass. |
 | 2026-02-09 | Codex | Step 137: Composition builder panel with pipeline generation and code insertion. 4/4 tests pass. |
 | 2026-02-09 | Codex | Step 138: Type-aware C++ generation via library call mappings. 2/2 tests pass. |
+| 2026-02-09 | Codex | Step 139: Library compatibility matrix with default mappings. 3/3 tests pass. |
 | 2026-02-09 | Codex | Added FEATURE_REQUESTS.md to track security vulnerability awareness and semantic library annotations for future sprints. |
 | 2026-02-09 | Codex | Added LLM tooling + MCP bridge feature request to FEATURE_REQUESTS.md. |
diff --git a/editor/CMakeLists.txt b/editor/CMakeLists.txt
index d55e566..c86208e 100644
--- a/editor/CMakeLists.txt
+++ b/editor/CMakeLists.txt
@@ -770,6 +770,10 @@ add_executable(step138_test tests/step138_test.cpp)
 target_include_directories(step138_test PRIVATE src)
 target_link_libraries(step138_test PRIVATE nlohmann_json::nlohmann_json)
 
+add_executable(step139_test tests/step139_test.cpp)
+target_include_directories(step139_test PRIVATE src)
+target_link_libraries(step139_test PRIVATE nlohmann_json::nlohmann_json)
+
 find_package(SDL2 CONFIG REQUIRED)
 find_package(OpenGL REQUIRED)
 find_package(glad CONFIG REQUIRED)
diff --git a/editor/src/LibraryCompatibility.h b/editor/src/LibraryCompatibility.h
new file mode 100644
index 0000000..389c4e9
--- /dev/null
+++ b/editor/src/LibraryCompatibility.h
@@ -0,0 +1,38 @@
+#pragma once
+#include <string>
+#include <unordered_map>
+#include <vector>
+
+class LibraryCompatibility {
+public:
+    void addMapping(const std::string& fromLibrary,
+                    const std::string& fromLang,
+                    const std::string& toLibrary,
+                    const std::string& toLang) {
+        mappings_[key(fromLibrary, fromLang)].push_back({toLibrary, toLang});
+    }
+
+    std::vector<std::pair<std::string, std::string>> getMappings(
+        const std::string& fromLibrary,
+        const std::string& fromLang) const {
+        auto it = mappings_.find(key(fromLibrary, fromLang));
+        if (it == mappings_.end()) return {};
+        return it->second;
+    }
+
+    void loadDefaultMappings() {
+        addMapping("numpy", "python", "Eigen", "cpp");
+        addMapping("numpy", "python", "ndarray", "rust");
+        addMapping("pandas", "python", "dataframe", "rust");
+        addMapping("pandas", "python", "DataFrame", "cpp");
+        addMapping("requests", "python", "reqwest", "rust");
+        addMapping("requests", "python", "cpr", "cpp");
+    }
+
+private:
+    static std::string key(const std::string& lib, const std::string& lang) {
+        return lib + "|" + lang;
+    }
+
+    std::unordered_map<std::string, std::vector<std::pair<std::string, std::string>>> mappings_;
+};
diff --git a/editor/tests/step139_test.cpp b/editor/tests/step139_test.cpp
new file mode 100644
index 0000000..46c90e6
--- /dev/null
+++ b/editor/tests/step139_test.cpp
@@ -0,0 +1,43 @@
+// Step 139 TDD Test: Library compatibility matrix
+#include "LibraryCompatibility.h"
+#include <iostream>
+
+static void expect(bool cond, const std::string& name, int& passed, int& failed) {
+    if (cond) {
+        std::cout << "Test " << (passed + failed + 1) << " PASS: " << name << "\n";
+        ++passed;
+    } else {
+        std::cout << "Test " << (passed + failed + 1) << " FAIL: " << name << "\n";
+        ++failed;
+    }
+}
+
+int main() {
+    int passed = 0;
+    int failed = 0;
+
+    LibraryCompatibility compat;
+    compat.loadDefaultMappings();
+    auto mappings = compat.getMappings("numpy", "python");
+    expect(!mappings.empty(), "numpy mappings present", passed, failed);
+    bool hasEigen = false;
+    for (const auto& entry : mappings) {
+        if (entry.first == "Eigen" && entry.second == "cpp") {
+            hasEigen = true;
+        }
+    }
+    expect(hasEigen, "numpy -> Eigen mapping", passed, failed);
+
+    compat.addMapping("numpy", "python", "armadillo", "cpp");
+    auto mappings2 = compat.getMappings("numpy", "python");
+    bool hasArma = false;
+    for (const auto& entry : mappings2) {
+        if (entry.first == "armadillo" && entry.second == "cpp") {
+            hasArma = true;
+        }
+    }
+    expect(hasArma, "custom mapping added", passed, failed);
+
+    std::cout << "\n=== Step 139 Results: " << passed << " passed, " << failed << " failed ===\n";
+    return failed == 0 ? 0 : 1;
+}
diff --git a/sprint5_plan.md b/sprint5_plan.md
index a50680e..b2d124d 100644
--- a/sprint5_plan.md
+++ b/sprint5_plan.md
@@ -146,7 +146,7 @@ what's already available.
   Cross-language projection respects library type mappings.
   *Modifies:* `CrossLanguageProjector.h`, `Generator.h`
 
-- [ ] **Step 139: Library compatibility matrix**
+- [x] **Step 139: Library compatibility matrix**
   Track which libraries have equivalents across languages. Example:
   `numpy` (Python) ↔ `Eigen` (C++) ↔ `ndarray` (Rust).
   When projecting code cross-language, suggest equivalent libraries.