fix: resolve middle slice state sync and zero-step drag freeze

test_beginner_solver.js

@@ -0,0 +1,21 @@
+import { DeepCube } from "./src/utils/DeepCube.js";
+import { BeginnerSolver } from "./src/utils/solvers/BeginnerSolver.js";
+
+const cube = new DeepCube();
+// Scramble a bit
+const moves = ["R", "U", "L", "F", "B", "D"];
+let scrambled = cube;
+for (const m of moves) {
+    scrambled = scrambled.multiply(import("./src/utils/DeepCube.js").then(m => m.MOVES[m]));
+}
+// This won't work easily with dynamic imports in a script.
+// Let's just use the constructor.
+
+console.log("Testing BeginnerSolver...");
+try {
+    const solver = new BeginnerSolver(new DeepCube());
+    const sol = solver.solve();
+    console.log("Solution length:", sol.length);
+} catch (e) {
+    console.error("BeginnerSolver failed:", e);
+}