diff --git a/sdk/package.json b/sdk/package.json
index 1b61167..86057d7 100644
--- a/sdk/package.json
+++ b/sdk/package.json
@@ -6,7 +6,8 @@
   "scripts": {
     "build": "node build.mjs",
     "test": "vitest run",
-    "checksize": "node build.mjs && gzip -c dist/v1.js | wc -c"
+    "typecheck": "tsc --noEmit",
+    "checksize": "node build.mjs && node -e \"const z=require('zlib'),f=require('fs');console.log('gzip bytes:',z.gzipSync(f.readFileSync('dist/v1.js')).length)\""
   },
   "devDependencies": {
     "esbuild": "^0.24.0",
diff --git a/sdk/src/util.ts b/sdk/src/util.ts
index 5bcc114..157c5e6 100644
--- a/sdk/src/util.ts
+++ b/sdk/src/util.ts
@@ -1,5 +1,6 @@
 export function uuid(): string {
-  if (globalThis.crypto?.randomUUID) return crypto.randomUUID();
+  const c = globalThis.crypto as Crypto | undefined;
+  if (c?.randomUUID) return c.randomUUID();
   return "xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx".replace(/[xy]/g, (c) => {
     const r = (Math.random() * 16) | 0;
     return (c === "x" ? r : (r & 0x3) | 0x8).toString(16);
diff --git a/sdk/test/util.test.ts b/sdk/test/util.test.ts
index 7cf9507..aceefb3 100644
--- a/sdk/test/util.test.ts
+++ b/sdk/test/util.test.ts
@@ -1,4 +1,4 @@
-import { describe, it, expect } from "vitest";
+import { describe, it, expect, vi } from "vitest";
 import { uuid } from "../src/util";
 describe("uuid", () => {
   it("生成 36 位且不重复", () => {
@@ -6,4 +6,11 @@ describe("uuid", () => {
     expect(a).toMatch(/^[0-9a-f-]{36}$/);
     expect(a).not.toBe(b);
   });
+  it("Math.random 降级分支：格式正确且唯一", () => {
+    vi.stubGlobal("crypto", {});
+    const a = uuid(), b = uuid();
+    expect(a).toMatch(/^[0-9a-f-]{36}$/);
+    expect(a).not.toBe(b);
+    vi.unstubAllGlobals();
+  });
 });
diff --git a/sdk/tsconfig.json b/sdk/tsconfig.json
index 05ebb33..77f6b7a 100644
--- a/sdk/tsconfig.json
+++ b/sdk/tsconfig.json
@@ -1,6 +1,7 @@
 {
   "compilerOptions": {
     "target": "ES2018",
+    "lib": ["ES2018", "DOM"],
     "module": "ESNext",
     "moduleResolution": "bundler",
     "strict": true,