We are going to create a single-page web app in one file: index.html
 We have three.min.js in the current directory, so we can include it with <script src="three.min.js"></script>
 The app should have:
   - A 3D Rubik's Cube that can be rotated by clicking on faces (or perhaps by dragging? But the requirement says clickable face rotations)
   - An orbit-drag camera (so we can use OrbitControls from three.js)
   - A scramble button that randomizes the cube state and animates the scrambling

 Steps:
 1. We'll set up a basic Three.js scene with a camera, renderer, and OrbitControls.
 2. Create the Rubik's Cube as a group of 27 smaller cubes (3x3x3). Each cubelet will be a mesh with a box geometry and materials for each face.
 3. We need to assign different colors to each face of the cubelets that are on the outer faces of the cube.
 4. Implement a way to rotate a face when it is clicked. We'll need raycasting to detect which face was clicked.
 5. The rotation should be animated and should update the internal state of the cube.
 6. Implement a scramble button that triggers a series of random rotations.

 Important: The entire app must be in one file: index.html, with CSS in a <style> tag and JS in a <script> tag.

 We'll structure the HTML file with:
   - A <div> for the renderer
   - A <button> for scrambling

 Since we are including three.min.js, we assume that THREE is available globally.

 We'll also include OrbitControls from the three.js examples. However, note that OrbitControls is not included in three.min.js. We have two options:
   a) If we have the OrbitControls source file in the current directory, we can include it separately (but the problem says we have only three.min.js).
   b) Alternatively, we can include the OrbitControls code inline? But that would be large.

 Since the requirement says "pre-provided three.min.js", and we are allowed to use files already present, but we don't have OrbitControls separately, we must reconsider.

 However, note: the requirement says "These library file(s) are ALREADY present in the current directory — load each with a plain <script src="NAME"></script> using its exact filename". We only have three.min.js, so we cannot include OrbitControls unless we also have it.

 But the problem does not mention OrbitControls being present. So we have two choices:
   Option 1: Implement a simple orbit-drag camera without OrbitControls? That would be complex.
   Option 2: Since OrbitControls is a common three.js addon, we might have it? But the problem says only three.min.js is present.

 Let me re-read: "These library file(s) are ALREADY present in the current directory — load each with a plain <script src="NAME"></script> using its exact filename (never a CDN or URL), then build on top of it: three.min.js."

 So only three.min.js is provided. Therefore, we cannot use OrbitControls unless we include its source inline? But that would violate the requirement of not using external resources? And OrbitControls is part of the three.js examples, which we don't have.

 Alternative: We can write a simple orbit control ourselves? But that might be too time-consuming and error-prone.

 However, note: the requirement says "orbit-drag camera", which is exactly what OrbitControls does. So we need it.

 Since we are allowed to write the entire app in one file, we can include the source code of OrbitControls in our script? But that would be copying a lot of code and might be messy.

 Alternatively, we can ask: is OrbitControls available? But the problem says only three.min.js is present.

 Given the constraints, I think we have to assume that we can use OrbitControls if we include it from the three.js examples? But we don't have it.

 We must stick to the requirement: only files present. So if we don't have OrbitControls, we cannot use it.

 Therefore, we must implement a simple version ourselves? Or perhaps the requirement allows us to include OrbitControls if we put it in the same directory? But we are not allowed to write multiple files? Only index.html.

 How about we include the OrbitControls source code inline in our script? We can copy the minified version? But note: we are not allowed to use external resources. So we would have to copy the entire OrbitControls code into our script.

 Considering the complexity, I think it's acceptable to include the OrbitControls source as a string in our script? But that would make the code very long.

 Alternatively, we can use a simpler method: use the built-in THREE.OrbitControls if it's available? But three.min.js doesn't include it.

 Since the problem states that we have three.min.js, and we don't have OrbitControls, we must do without? Or we can write a minimal version.

 However, note: the problem says "pre-provided three.min.js", and we are building on top of it. We are allowed to write any code we want in the script. So we can write our own orbit controls? But that is a big task.

 Let me check: OrbitControls is about 1000 lines? We don't want to include that.

 Given the complexity, I think we can use a simpler drag-to-rotate camera. We can implement a basic version with mouse events and rotating the camera around the cube.

 We'll do:
   - On mouse down, record the position.
   - On mouse move, calculate the difference and rotate the camera around the cube.

 But the requirement says "orbit-drag camera", which usually allows pan, zoom, and rotate. We can implement a basic one.

 Alternatively, we can look for a minimal OrbitControls implementation? But that might be beyond the scope.

 Since the main focus is the Rubik's cube, we can implement a very basic camera rotation with mouse drag? Without zoom and pan? Or just rotation.

 We'll do:
   - Camera positioned at (5,5,5) looking at (0,0,0)
   - On drag, rotate the camera around the cube in the horizontal and vertical.

 Steps for camera:
   - Add event listeners for mousedown, mousemove, mouseup.
   - On mousedown: set a flag and record mouse position.
   - On mousemove: if flag is set, calculate the change in mouse position and update the camera's rotation around the cube.
   - We'll use spherical coordinates for the camera.

 However, to save time and complexity, I found that three.min.js does not include OrbitControls, so we'll write a minimal version.

 But note: the requirement says "orbit-drag camera", meaning the user can drag to orbit around the cube. We'll implement a simple one.

 Alternatively, we can omit OrbitControls and just use the built-in camera controls? There are none.

 Given the time, I will implement a simple drag-to-rotate camera.

 Plan for the Rubik's cube:

 1. Create 27 cubelets (from -1 to 1 in x, y, z).
    Each cubelet will be a Mesh with a BoxGeometry and an array of 6 materials (one for each face). For inner faces, we use a neutral color? But the Rubik's cube only shows the outer faces.

    Actually, we only need to color the outer faces of the entire cube. For each cubelet, we assign:
        - If the cubelet is on the front face (z=1), then the front face material is the front color (e.g., green).
        - Similarly for back (z=-1): blue? and so on.

    The standard colors for a Rubik's cube:
        front: green
        back: blue
        left: orange
        right: red
        top: white
        bottom: yellow

    For cubelets that are not on the outer face, we set the corresponding face to black? Or gray? Let's use dark gray for inner faces.

 2. We'll create a group for the entire cube.

 3. For rotation: we need to know which face was clicked. We can use raycasting to find the cubelet and the face normal. Then we determine which face of the entire cube that normal corresponds to (e.g., if the normal is (0,0,1) then it's the front face).

 4. When a face is clicked, we rotate all cubelets that belong to that face (e.g., all with z=1) around the cube's center in the plane of that face.

 5. We'll animate the rotation over a short period.

 6. We need to update the internal state of the cube. We can represent the cube as a 3x3x3 array of cubelet objects? But note: after rotations, cubelets move. We must update their positions and orientations.

 7. Instead of physically moving the cubelets, we can keep the group structure and rotate the entire face group? But then we have to update the positions of the cubelets in the group? Alternatively, we can use a group per face rotation? But that complicates the hierarchy.

 8. Alternatively, we can use a single group for the entire cube and update the positions and orientations of the cubelets after each rotation? But that would break the grouping.

 9. Better: we can use a group for each cubelet? Then when rotating a face, we can take the 9 cubelets of that face and put them in a temporary group, rotate the group, then break the group and update the positions? But that is complex.

 10. Another method: we can use a transformation matrix for each cubelet? But then we have to manage the state.

 11. Instead, we can store the cube state as a 3x3x3 array of objects that have:
        position: {x, y, z} in integers (from -1 to 1)
        orientation: quaternion? or we can track the rotations applied? 

 12. However, for simplicity, we can just update the positions and rotations of the cubelet meshes and then update our state array accordingly? But note: after multiple rotations, the state array must reflect the current permutation.

 13. Alternatively, we can use a group for the entire cube and then when rotating a face, we apply a rotation to each cubelet that belongs to that face? Then update the world matrix? But then we have to update our state.

 14. We'll represent the cube state as a 3D array (size 3x3x3) of cubelet objects. Each cubelet has:
        mesh: the THREE.Mesh
        originalPosition: the initial position (which is also the solved position)
        currentPosition: the current position (which might be different after rotations)
        currentRotation: the current rotation (as a quaternion or euler) relative to the original orientation.

 15. But note: when we rotate a face, we are going to rotate the cubelets around the cube's center. We can calculate the new position and rotation for each cubelet in the face.

 16. We'll create an array `cubelets` of 27 meshes, and we also create a 3D array `cubeState` of size 3x3x3 that holds references to the cubelets at each position.

 17. When rotating a face (say, front face), we take all cubelets with z=1 (if front is z=1) and apply a rotation around the z-axis? Actually, we rotate around the axis perpendicular to the face? For front face, we rotate around the z-axis? But the rotation axis should be the center of the face and pointing out? Actually, we rotate around the cube's center? The cube's center is (0,0,0). The front face is at z=1, so we want to rotate around the center of the front face? But the center of the front face is (0,0,1). So we need to rotate around the axis that goes through (0,0,1) and is parallel to the z-axis? Actually, no: we want to rotate the entire face around the cube's center? But the cube's center is (0,0,0). The face is at z=1, so we rotate around the z-axis? But that would rotate the entire cube? We want only the face.

 18. Actually, we want to rotate the 9 cubelets of the front face around the axis that goes through the center of the cube and is perpendicular to the face? But that axis is the z-axis? Then we rotate the cubelets around the z-axis by 90 degrees? But that would move them in the x-y plane? And also change their positions? 

 19. Example: a cubelet at (1,1,1) rotated 90 degrees around the z-axis (at the origin) would go to (-1,1,1). But that is not correct because we want the front face to rotate in place? Actually, we want to rotate the face around the center of the face, not the cube's center.

 20. So we should rotate the cubelets around the center of the face? For the front face, center is (0,0,1). We can create a rotation matrix around the axis (0,0,1) and then rotate each cubelet around that point? But note: the cubelet at (1,1,1) rotated 90 degrees around the z-axis at (0,0,1) would go to (1,-1,1)? Actually, let's compute:

        Point: (1,1,1)
        Rotate 90 degrees counterclockwise around (0,0,1) in the xy plane:
            relative vector: (1,1,1) - (0,0,1) = (1,1,0)
            rotate (1,1,0) by 90 degrees: (-1,1,0)
            then new position: (0,0,1) + (-1,1,0) = (-1,1,1)

        But (-1,1,1) is the position of the cubelet that was originally at (1,1,1)? Actually, no: the original positions are integers from -1 to 1. So (-1,1,1) is a valid position.

 21. So we can do: for each cubelet in the face, we set a new position by rotating it around the face center by 90 degrees.

 22. We'll do the rotation in the animation: we don't change the state until the animation is done.

 23. Steps for rotating a face:
        a) Identify the face by the normal (or by the axis and direction).
        b) Determine the face center: for front (z=1): (0,0,1); back (z=-1): (0,0,-1); left (x=-1): (-1,0,0); etc.
        c) Determine the rotation axis: for front/back: z-axis, for left/right: x-axis, for top/bottom: y-axis? Actually, for front: we rotate around the z-axis? But the rotation axis for the face is the normal? So for front, the rotation axis is (0,0,1). But when we rotate, we want to rotate in the plane of the face? So the axis of rotation is the normal? Then we rotate around that axis? But then the rotation would be in the plane? Yes.

        d) We'll rotate by 90 degrees clockwise or counterclockwise? We can decide based on the click? Or we can always rotate clockwise? Actually, the user doesn't specify direction? The requirement says "clickable face rotations", but doesn't specify direction. So we can do clockwise? Or we can rotate in the direction that feels natural? Let's do clockwise when looking at the face.

        e) We create a rotation matrix that rotates around the face center? Actually, we can use:

            cubelet.position.sub(faceCenter).applyAxisRotation(axis, angle).add(faceCenter);

        f) And also rotate the cubelet's quaternion by the same rotation? So that the colors are oriented correctly.

 24. However, note: the cubelet has its own rotation? Initially, they are all identity. When we rotate the entire cubelet, we update both position and rotation.

 25. After the animation, we update the state array: we swap the cubelets in the 3D array? Actually, we reassign the positions.

 26. For scrambling: we generate a sequence of random face rotations and animate them one after the other.

 Implementation:

 We'll create:
   - Scene, camera, renderer
   - A group for the cube
   - 27 cubelets, each with:
        geometry: new THREE.BoxGeometry(0.95, 0.95, 0.95) (so there's a gap)
        materials: an array of 6 materials. For each face of the cubelet, we assign a color based on the cubelet's original position.

        How to assign colors?
          For a cubelet at (x,y,z):
            - If z === 1, then the front face (index 4? note: three.js BoxGeometry faces: 0: right, 1: left, 2: top, 3: bottom, 4: front, 5: back) -> but wait, the order might be different? Actually, we can set:

            We'll create an array of materials for the 6 faces:

            materials[0] = right face: if x === 1 ? red : innerColor
            materials[1] = left face: if x === -1 ? orange : innerColor
            materials[2] = top face: if y === 1 ? white : innerColor
            materials[3] = bottom face: if y === -1 ? yellow : innerColor
            materials[4] = front face: if z === 1 ? green : innerColor
            materials[5] = back face: if z === -1 ? blue : innerColor

        But note: the face indices in BoxGeometry are:
            0: right
            1: left
            2: top
            3: bottom
            4: front
            5: back

        So we assign accordingly.

   - Add each cubelet to the cube group.

   - We'll store the cubelets in a flat array and also in a 3D array: cubeState[i][j][k] for position (x,y,z) where:
        i = x+1 (0 to 2)
        j = y+1 (0 to 2)
        k = z+1 (0 to 2)

 27. Raycasting: when the user clicks, we cast a ray from the mouse position and find the first cubelet intersected. Then we get the face of the cubelet that was hit (using `face` in the intersection). Then we determine which face of the entire cube that corresponds to? Actually, the face of the cubelet might be one of the six, and we can map the normal to a face of the entire cube.

        Example: if the normal is (0,0,1), then it's the front face of the entire cube? But note: the cubelet might be at the front, so yes.

        However, if the cube is rotated, the cubelet's normal is in world coordinates? We can use the normal in world space.

        We'll convert the normal to a standard direction? We can round the normal to the nearest axis.

        Steps:
          - Get the intersection point and the face normal (in world coordinates).
          - Normalize the normal and round to the nearest axis-aligned vector? e.g., (0.23, -0.97, 0.1) -> (0,-1,0) -> bottom face.

        Then we know which face of the entire cube was clicked? Actually, the face of the entire cube is defined by the axis and the direction? For example, the bottom face is all cubelets with y=-1.

        So we can map the normal to:
          (1,0,0) -> right face
          (-1,0,0) -> left face
          (0,1,0) -> top face
          (0,-1,0) -> bottom face
          (0,0,1) -> front face
          (0,0,-1) -> back face

        Then we rotate that entire face.

 28. Animation: we'll use requestAnimationFrame to animate the rotation over 0.5 seconds? We'll rotate the cubelets of the face around the face center by 90 degrees.

 29. During the animation, we should disable further clicks? Or queue them.

 30. Scramble button: when clicked, generate a sequence of say 20 random moves (each move: pick a random face and a random direction) and then animate them one after the other.

 31. We'll create a queue for animations? Or use promises? We can use a simple callback chain.

 Given the complexity, we'll break the code into functions.

 We'll write the entire code in one script tag.

 Let's start writing the HTML file.

 Note: We must not use external resources, so we'll inline everything.

 Steps for the HTML:

   <!DOCTYPE html>
   <html>
   <head>
     <title>Rubik's Cube</title>
     <style>
        body { margin: 0; }
        canvas { display: block; }
        #controls { position: absolute; top: 10px; left: 10px; }
     </style>
   </head>
   <body>
     <div id="container"></div>
     <div id="controls">
        <button id="scramble">Scramble</button>
     </div>

     <script src="three.min.js"></script>
     <script>
        // Our code here
     </script>
   </body>
   </html>

 Now, the JavaScript code:

   We'll define:
     - Variables for scene, camera, renderer, cube group, cubeState, etc.
     - Sizes for the cubelet and gap.

   Steps in the script:

     1. Set up the scene, camera, renderer.
     2. Create the cube group and cubelets.
     3. Add lights (ambient and directional).
     4. Set up raycasting and mouse interaction.
     5. Implement the rotateFace function that animates a face rotation.
     6. Implement the scramble function.

   Due to the complexity, we'll write a simplified version.

   Note: We are not going to implement a full Rubik's cube solver state, but we will update the positions of the cubelets in the cubeState array after each rotation.

   We'll represent the cubeState as a 3D array (3x3x3) of objects that have:
        mesh: the THREE.Mesh
        position: the current integer position (x,y,z) in [-1,0,1]

   Initially, the cubeState[i][j][k] corresponds to the cubelet at:
        x = i-1, y = j-1, z = k-1

   After a rotation, we reassign the cubelets in the rotated face to their new positions.

   Steps for rotating a face (e.g., front face: z=1):

        We take all cubelets with current position z=1.

        We want to rotate them 90 degrees clockwise around the face center (0,0,1) in the xy plane? Actually, clockwise when looking from the front? That would be clockwise around the positive z-axis? But note: three.js uses right-handed coordinate system, so positive rotation is counterclockwise? We want clockwise? Then we use -Math.PI/2.

        The rotation matrix for a 2D rotation in the xy plane around (0,0,1) by -90 degrees (clockwise) is:
            x' = x * cos(-90) - y * sin(-90) = x*0 - y*(-1) = y
            y' = x * sin(-90) + y * cos(-90) = x*(-1) + y*0 = -x
            z remains the same.

        So new position: (x, y, z) becomes (y, -x, z)

        But note: we are rotating around (0,0,1), so we do:

            let relX = x - 0;
            let relY = y - 0;
            let newRelX = relX * cos(-90) - relY * sin(-90);
            let newRelY = relX * sin(-90) + relY * cos(-90);
            newX = newRelX + 0;
            newY = newRelY + 0;

        Which is: newX = y, newY = -x.

        So the cubelet at (1,1,1) becomes (1, -1, 1) -> (1, -1, 1) -> but note: (1,-1,1) is the position that was originally occupied by the cubelet at (1,1,1) becomes (1,-1,1)? Actually, we are reassigning the positions.

        We must update the cubeState: we create a temporary copy of the face, then assign the new positions.

        Example: the front face has 9 cubelets at positions (x,y,1) for x in [-1,0,1] and y in [-1,0,1].

        After clockwise rotation:
            (-1,-1,1) -> (-1,1,1) -> but wait: 
                (-1,-1) -> ( -1, 1 )? Let me compute:
                    x = -1, y = -1 -> newX = y = -1, newY = -x = 1 -> (-1,1,1)
            (0,-1,1) -> (-1,0,1) -> but wait: 
                x=0, y=-1 -> newX = -1, newY = 0 -> (-1,0,1)
            (1,-1,1) -> (-1,-1,1) -> no: 
                x=1, y=-1 -> newX = -1, newY = -1 -> (-1,-1,1)

            (-1,0,1) -> (0,1,1) -> 
                x=-1, y=0 -> newX=0, newY=1 -> (0,1,1)
            (0,0,1) -> (0,0,1) -> remains
            (1,0,1) -> (0,-1,1) -> 
                x=1, y=0 -> newX=0, newY=-1 -> (0,-1,1)

            (-1,1,1) -> (1,1,1) -> 
                x=-1, y=1 -> newX=1, newY=1 -> (1,1,1)
            (0,1,1) -> (1,0,1) -> 
                x=0, y=1 -> newX=1, newY=0 -> (1,0,1)
            (1,1,1) -> (1,-1,1) -> 
                x=1, y=1 -> newX=1, newY=-1 -> (1,-1,1)

        So we see that the cubelet at (1,1,1) moves to (1,-1,1) and so on.

        We can represent the transformation as:
            newX = y
            newY = -x

        Then we update the cubelet's position in the cubeState? Actually, we are going to physically move the cubelet's mesh to the new position? And update the cubeState array.

        Steps for updating:
            - Create a temporary array of the cubelets in the face.
            - For each cubelet in the face, calculate its new position (x', y', z) = (y, -x, z).
            - Then update the cubeState: set the old position to null, then set the new position to this cubelet.
            - Also update the cubelet's mesh position: we set it to (x', y', z) multiplied by the spacing? Our cubelets are spaced by 1 unit? So we set mesh.position.set(x', y', z).

        But note: during the animation, we are going to interpolate the position? Actually, we'll animate the rotation? We can either animate the position change or animate the rotation? We want to see the cubelets rotating? So we should animate by rotating the cubelets around the face center.

        How to animate:
            - We'll create an animation loop for the rotation.
            - For each cubelet in the face, we set a target rotation (90 degrees) and also a target position? But we can compute the intermediate rotation by applying a rotation matrix at each frame? 

        Alternatively, we can create a temporary group for the face? Then rotate the group? Then after the animation, break the group and update the positions? That might be easier.

        Steps:
            - Create a temporary group and add all cubelets of the face to it.
            - Position the group at the face center (0,0,1).
            - Then rotate the group around the axis (0,0,1) by 90 degrees? But note: we want to rotate the cubelets around the face center? So we set the group's position to (0,0,1) and then rotate the group? Then the cubelets will rotate around (0,0,1).

            - However, the cubelets are currently at positions relative to the world? So if we add them to the group, their positions become relative to the group? We must set the group's position to (0,0,1) and then set each cubelet's position relative to the group? We can subtract the face center.

            - We do:
                group.position.set(0,0,1);
                for each cubelet in the face:
                    cubelet.position.sub(faceCenter);   // faceCenter is (0,0,1) -> becomes (x,y,0)
                    group.add(cubelet);

            - Then we animate the group's rotation around the z-axis by 90 degrees? But note: we want to rotate by 90 degrees? So we set:
                group.rotation.z = targetAngle (in radians)

            - Then after the animation, we remove the cubelets from the group and add them back to the cube group? And set their positions to the new positions? And update the cubeState.

        This method avoids having to update the positions during the animation? But we still have to update the cubeState after.

        We'll do:

            let faceCenter = new THREE.Vector3(0,0,1); // for front face
            let group = new THREE.Group();
            group.position.copy(faceCenter);
            for (let cubelet of faceCubelets) {
                // cubelet is a mesh
                cubelet.position.sub(faceCenter);
                group.add(cubelet);
            }
            scene.add(group); // or cubeGroup.add(group)? But we removed them from cubeGroup? We should remove them from cubeGroup first.

            Then animate group.rotation.z from 0 to Math.PI/2 (for 90 degrees clockwise? Actually, clockwise is negative? Because three.js uses right-hand rule: positive rotation is counterclockwise. So clockwise is -Math.PI/2.

            Then after the animation, we remove the group and set the cubelet positions to the new positions? But note: after rotating the group by -90 degrees, the cubelet's local positions are rotated? So when we remove them, we have to set their world positions to the new integer positions? But we already know the new positions: (y, -x, 1) for each cubelet that was at (x,y,1).

            So we can do:
                After the animation, remove the cubelets from the group and add them back to the cubeGroup.
                Then set each cubelet's position to the new integer position (multiplied by the spacing? We use 1 unit per cubelet) and reset their rotation? Actually, we also need to update the cubelet's rotation: we apply the rotation to the cubelet's quaternion? Or we can set the cubelet's rotation to the accumulated rotation? But note: the cubelet might have been rotated before? We should not reset, but accumulate.

            Alternatively, we can avoid changing the cubelet's rotation and instead update their positions and then reset the rotation? But then the stickers would be oriented correctly? Actually, the cubelet's own rotation doesn't change? Only the group rotates? Then when we remove the cubelet, it retains its local rotation? So we must reset the rotation? 

            Actually, we can avoid this by not using a group? We can animate each cubelet individually? That might be simpler.

        Given the complexity, I'll animate each cubelet individually by rotating it around the face center.

        Steps for individual animation:

            For each cubelet in the face:
                let startPos = cubelet.position.clone();
                let endPos = new THREE.Vector3(y, -x, z); // for front face, but note: we are in world coordinates? And we want to rotate around (0,0,1)

                But we can compute the intermediate position by rotating the vector (startPos - faceCenter) around the axis (0,0,1) by an angle.

            We'll use a function to rotate a point around an axis by an angle? We can use:

                function rotatePoint(point, center, axis, angle) {
                    let q = new THREE.Quaternion();
                    q.setFromAxisAngle(axis, angle);
                    let v = point.clone().sub(center);
                    v.applyQuaternion(q);
                    return v.add(center);
                }

            Then in the animation loop, for each cubelet, we set:
                cubelet.position.copy(rotatePoint(startPos, faceCenter, axis, currentAngle));

            And also rotate the cubelet's quaternion? We can do:

                cubelet.quaternion.premultiply(q); // but note: we are rotating incrementally? So we should set a starting quaternion and then multiply by the delta?

            Actually, we can set the cubelet's rotation at each frame? Or we can set the cubelet's quaternion once at the start and then not change it? The cubelet's own rotation doesn't change? Only its position? But then the stickers would not rotate? We want the cubelet to rotate? So we should also rotate the cubelet.

            We'll do:
                cubelet.rotateOnWorldAxis(axis, anglePerFrame);

            But note: we are rotating around the face center, not the cubelet's center? So we have to set the position and rotation separately.

        This is complex.

        Given the time, we'll use the group method and then after the animation, we reset the cubelet's rotation and set their positions to the new integer positions? And update the cubeState.

        Steps for group method:

            - Remove the cubelets from the cubeGroup and add them to a temporary group.
            - Position the group at (0,0,1).
            - Set the cubelets' positions relative to the group (so subtract (0,0,1)).
            - Animate the group.rotation.z from 0 to -Math.PI/2 over 0.5 seconds.
            - After the animation, remove the cubelets from the group and add them back to the cubeGroup.
            - Set each cubelet's position to the new integer position (which we computed: (y, -x, 1)) and set their rotation to identity? But note: the cubelet might have been rotated by the group? Actually, the group rotation does not change the cubelet's local rotation? Only the group's transformation? So when we remove the cubelet, it is still at its local position (which is the original position relative to the group) and with its original rotation? So we must set the world position to the new integer position? And reset the rotation? 

            We can do:
                cubelet.position.set(y, -x, 1);
                cubelet.rotation.set(0,0,0);

            And update the cubeState.

        This will work.

 32. We'll implement the group method for animation.

 33. Scramble: we'll generate a sequence of moves and then execute them with delays between.

 34. We'll use a state variable `isAnimating` to prevent concurrent animations.

 35. Due to the complexity, we'll write the code step by step.

 Given the length, we'll write the code in the script tag.

 Let's start writing the code.

 Note: This is a simplified version and might not be fully optimized.

 We'll write the code in the following order:

   A. Set up the scene
   B. Create the cube
   C. Add event listeners for mouse and button
   D. Implement rotateFace function (using temporary group)
   E. Implement scramble function

 We'll assume the cube has 3x3x3 cubelets, each of size 1, with a small gap.

 Let's code.