Zauberwürfel, der sich selbst löst

> Create a single HTML file that uses Three.js to visualize a Rubik's Cube with realistic lighting and interactive controls. The cube should be built from 27 cubies with standard Rubik's Cube coloring. Include buttons for standard moves (U, U′, D, D′, L, L′, R, R′, F, F′, B, B′) that animate a 90° rotation on the appropriate face. Also, implement a scramble function that performs a series of random moves (recording each move), and an automatic unscrambler that, every 500 ms, applies the inverse of the recorded moves until the cube is solved. The solved state should be determined by comparing each cubie's current world position and rotation with its originally stored "solved" state (using a small tolerance). Use the following script sources:
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/controls/OrbitControls.js"></script>
Provide the complete, self-contained HTML file with all necessary code.