feat: reposition solver controls to a dropdown

Moved the Kociemba/Beginner solve options into a sleek dropdown menu positioned above the Scramble button on the left side of the screen. This ensures the solver controls no longer obstruct the programmatic move queue at the bottom.

test/verify_integrity.js

@@ -0,0 +1,41 @@
+import { DeepCube, MOVES } from "../src/utils/DeepCube.js";
+
+function runStressTest(iterations) {
+  console.log(`Starting DeepCube Stress Test (${iterations} moves)...`);
+
+  let cube = new DeepCube(); // Solved
+
+  const moveNames = Object.keys(MOVES);
+  const startTime = Date.now();
+
+  for (let i = 1; i <= iterations; i++) {
+    const randomMove = moveNames[Math.floor(Math.random() * moveNames.length)];
+    cube = cube.multiply(MOVES[randomMove]);
+
+    if (!cube.isValid()) {
+      console.error(`\n❌ INVALID STATE DETECTED AT MOVE ${i}!`);
+      console.error(`Move applied: ${randomMove}`);
+      console.error(`CP:`, cube.cp);
+      console.error(`CO:`, cube.co);
+      console.error(`EP:`, cube.ep);
+      console.error(`EO:`, cube.eo);
+      process.exit(1);
+    }
+
+    if (i % 100000 === 0) {
+      process.stdout.write(
+        `\r✅ ${i} moves verified (${((i / iterations) * 100).toFixed(0)}%)`,
+      );
+    }
+  }
+
+  const duration = Date.now() - startTime;
+  console.log(
+    `\n🎉 Success! Mathematical integrity held over ${iterations} random moves.`,
+  );
+  console.log(
+    `⏱️  Time taken: ${duration} ms (${(iterations / (duration / 1000)).toFixed(0)} moves/sec)`,
+  );
+}
+
+runStressTest(1000000);