Add login gate, calculation history, and AI markdown download.

Co-authored-by: Cursor <cursoragent@cursor.com>

app/api/auth/logout/route.ts

@@ -0,0 +1,14 @@
+import { NextResponse } from "next/server";
+import { SESSION_COOKIE } from "@/lib/auth/session";
+
+export async function POST() {
+  const res = NextResponse.json({ ok: true });
+  res.cookies.set(SESSION_COOKIE, "", {
+    httpOnly: true,
+    sameSite: "lax",
+    secure: process.env.NODE_ENV === "production",
+    path: "/",
+    maxAge: 0,
+  });
+  return res;
+}