The user wants me to create a single-page web app that renders an interactive 3D Rubik's Cube using Three.js. The requirements are:

1. Use the provided three.min.js file (global THREE)
2. Interactive 3D Rubik's Cube
3. Clickable face rotations
4. Orbit-drag camera
5. Scramble button
6. Everything in one self-contained index.html file
7. No external resources, CDNs, or network requests

Let me create this interactive Rubik's Cube:

1. Set up the scene, camera, and renderer
2. Create a 3x3x3 Rubik's Cube structure (27 small cubes, but we only see the outer ones)
3. Make it interactive - clicking on faces to rotate layers
4. Add orbit controls for camera rotation
5. Add a scramble button

Let me write this comprehensive HTML file.

I've created the index.html file with a complete 3D Rubik's Cube interactive application. Let me verify it was created properly and check that it has all the required features.

The file includes:
1. Three.js loading from the local three.min.js file
2. A 3x3x3 Rubik's Cube with proper colors for each face
3. Orbit-drag camera controls (click and drag to rotate around the cube)
4. Clickable face rotations (click on cube faces to rotate layers)
5. A scramble button that randomizes the cube
6. A reset button to restore the cube to solved state
7. All CSS inline in a <style> tag
8. All JS inline in a <script> tag
9. No external CDNs or network requests

Let me verify the file exists.

The file was created successfully. The index.html file is 19235 bytes and is now present in the current directory. The application includes:

1. **3D Rubik's Cube** - A complete 3x3x3 cube with proper colors (Red, Orange, White, Yellow, Green, Blue)
2. **Orbit-drag camera** - Click and drag on the canvas to rotate the camera around the cube
3. **Clickable face rotations** - Click on cube faces to rotate the corresponding layers
4. **Scramble button** - Randomizes the cube with 20 random moves
5. **Reset button** - Returns the cube to its solved state
6. **All self-contained** - CSS in <style>, JS in <script>, loads three.min.js locally
7. **No external resources** - Uses only the provided three.min.js file

The implementation includes:
- Proper lighting with ambient and directional lights
- Smooth animations with easing functions
- Raycasting for accurate click detection on cube faces
- Camera controls that update spherical coordinates
- State management for tracking cube positions and rotations
- Responsive design with a gradientbackground