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.

src/utils/CubeLogicAdapter.js

@@ -0,0 +1,59 @@
+import { DeepCube, MOVES } from './DeepCube.js';
+import { CubeModel } from './CubeModel.js';
+
+export class RubiksJSModel {
+  constructor() {
+    this.state = new DeepCube();
+    this.visual = new CubeModel();
+  }
+
+  reset() {
+    this.state = new DeepCube();
+    this.visual = new CubeModel();
+  }
+
+  rotateLayer(axis, index, dir, steps = 1) {
+    let move = '';
+    if (axis === 'y') {
+      if (index === 1) move = dir === 1 ? "U'" : "U";
+      else if (index === -1) move = dir === -1 ? "D'" : "D";
+    } else if (axis === 'x') {
+      if (index === 1) move = dir === 1 ? "R'" : "R";
+      else if (index === -1) move = dir === -1 ? "L'" : "L";
+    } else if (axis === 'z') {
+      if (index === 1) move = dir === 1 ? "F'" : "F";
+      else if (index === -1) move = dir === -1 ? "B'" : "B";
+    }
+
+    if (move) {
+      for (let i = 0; i < steps; i++) {
+        try {
+          this.state = this.state.multiply(MOVES[move]);
+        } catch (e) {
+          console.error('[RubiksJSModel] Failed to apply move:', move, e);
+        }
+        this.visual.rotateLayer(axis, index, dir);
+      }
+    }
+  }
+
+  applyTurn(move) {
+    if (!move) return;
+    try {
+      this.state = this.state.multiply(MOVES[move]);
+    } catch (e) {
+      console.error('[RubiksJSModel] Failed to apply direct move:', move, e);
+    }
+    this.visual.applyMove(move);
+  }
+
+  toCubies() {
+    return this.visual.toCubies();
+  }
+
+  validate() {
+    const valid = this.state.isValid();
+    return { valid, errors: valid ? [] : ['Invalid cube configuration (Parity or Orientation rules violated)'] };
+  }
+}
+