fix live analysis multi-device lock

server/_core/sdk.ts

@@ -4,6 +4,7 @@ import axios, { type AxiosInstance } from "axios";
 import { parse as parseCookieHeader } from "cookie";
 import type { Request } from "express";
 import { SignJWT, jwtVerify } from "jose";
+import { createHash } from "node:crypto";
 import type { User } from "../../drizzle/schema";
 import * as db from "../db";
 import { ENV } from "./env";
@@ -223,11 +224,15 @@ class SDKServer {
         return null;
       }
 
+      const derivedSid = typeof sid === "string" && sid.length > 0
+        ? sid
+        : `legacy-token:${createHash("sha256").update(cookieValue).digest("hex").slice(0, 32)}`;
+
       return {
         openId,
         appId,
         name: typeof name === "string" ? name : undefined,
-        sid: typeof sid === "string" ? sid : undefined,
+        sid: derivedSid,
       };
     } catch (error) {
       console.warn("[Auth] Session verification failed", String(error));