Rubik's Cube · qwen3.8-flash

Let me start by exploring the working directory.

Three.js r1xx (2021) — likely r132-ish. Let me check the version string.

Let me plan the implementation:

- Build a 3x3 cube from 27 cubies (small cubes) each with per-face colored materials using a materials array (6 materials per mesh, using face material indices). In newer Three.js, BoxGeometry has groups so material arrays work.
- Stickers: Instead of coloring whole cubie faces, better to add slightly inset sticker planes on each cubie's outer faces for visible boundaries. But simpler: use dark base material for cubie body + sticker meshes (PlaneGeometry) offset outward. Sticker meshes are children of the cubie group so they move with it. That preserves state through moves naturally since the actual 3D objects rotate/move.

Implementation approach for moves:
- Maintain array of cubies with their group objects (THREE.Group per cubie, containing body mesh + sticker meshes).
- For a move: select cubies with coordinate along the axis matching the layer, parent them to a temporary pivot group aligned with axis, animate pivot rotation from 0 to ±90°, then on completion bake: for each cubie, apply the pivot's final matrix to world matrix, reattach to scene root, round positions to integers, set quaternion from rounded rotation matrix. This keeps state accurate.

Also track logical state (for scramble and verification of sticker arrangement) — but the geometry-based approach is inherently state-preserving. For verification, I could compute a state representation from sticker world positions/normals.

Camera controls: implement own orbit controls (spherical coords, drag on background rotates camera around origin). Wheel zoom with min/max distance bounds. Need to distinguish dragging background vs. turning a face. The requirement says "Dragging the background orbits the camera without turning a face." So dragging on a face should turn the face? That's implied — dragging on the cube could do a face turn (nice bonus). Requirement: dragging the background orbits camera without turning a face. I'll implement: raycast on pointerdown; if hit a cubie sticker/body, then on drag we perform a face quarter turn (drag-based turning); if no hit, orbit. That gives a rich implementation, and background drag orbit is required.

Drag-to-turn: compute the sticker face normal at hit point, and the drag vector in 3D. Standard approach: get hit point, project camera drag direction into the plane of the face, determine the tangential axis among cube axes, then the rotation axis = faceNormal × dragAxis, and direction sign accordingly. Implement simplified: after pointer move accumulation exceeding threshold, compute the 3D displacement of the drag ray intersection projected onto the face plane; determine the dominant in-plane cube axis; then axis = cross(normal, dragAxis) mapped to one of x/y/z; angle sign determined by matching rotation direction of drag.

Let me be careful but keep it reasonably simple. Actually, since only background-orbit is strictly required, drag-turning is a bonus. I'll implement it since it's nice, but with robust fallbacks (if computed mapping fails, ignore).

UI: buttons for U, U', D, D', L, L', R, R', F, F', B, B'. Plus scramble and reset. Show move counter, timer maybe. Also keyboard shortcuts.

Face color scheme (standard): U=white (top, +y), D=yellow (down, -y), F=green (+z), B=blue (-z), R=red (+x), L=orange (-x).

Mapping moves to axes:
- U/D: rotate about Y axis. U = clockwise looking down at top face = rotation about +Y by -90°? Let's define: U turn is clockwise when viewed from above (from +Y looking toward -Y). A rotation about +Y by angle θ (right-hand rule, counterclockwise when viewed from +Y looking down at origin i.e. from above). Rotating about +Y with positive θ moves +Z toward +X? Let's compute: R_y(θ) maps (x,z): x' = x cosθ + z sinθ, z' = -x sinθ + z cosθ. For θ=+90°: point at +Z (0,0,1) → x'=1, z'=0 → +X. So +Z→+X, +X→-Z. Viewed from above (+Y looking down): we see the XZ plane. With standard view from above where screen-right = +X and screen-down = ... hmm. Looking down -Y, if we set up = -Z (so north/away = -Z, south/toward viewer bottom = +Z) — depends. Let's just verify with a concrete check: Front face center (0,0,1) — top layer of U move is the front-top row... Actually easier: define moves in terms of the resulting permutation, and verify programmatically with the app logic by testing a move + inverse returns to identity, and also check the cycle of facelets for a known scramble pattern.

Simplest: Define U as rotation about +Y of -90° (i.e. -PI/2) and check what cycle that yields: R_y(-90°) maps +Z→-X? Using above: θ=-90: x' = x*0 + z*(-1) = -z; z' = -x*(-1) + z*0 = x. So (0,0,1)→(-1,0,0) = -X = L face direction. So front→left. Standard U (clockwise from above): front face's top row goes to the left face. Let's check: hold cube with F green facing you, U face white. Turn U clockwise (viewed from above): the front-top cubie moves to the left-top position. Yes — clockwise from above when looking down with front toward you (south). Looking from top down, front (+Z) appears at the bottom of your view, right (+X) at your... when looking straight down with head oriented normally, +X (right) appears on your left? Hmm. Let's use a concrete standard: In standard notation with the cube viewed with U on top facing you (looking from +Y down), F is toward the viewer (down on screen). Looking from above: the direction to +Z (front, toward original viewer) points... We're looking along -Y. Choose screen x-axis = +X (world right), then screen y-axis must satisfy view direction -Y = screen_x × screen_y? For a right-handed view: view direction (into screen) = -(screenX × screenY)... Let me just do it with vectors: observer at +Y looking toward origin. Camera forward = (0,-1,0). Camera up roughly = (0,0,-1) (so that the far side, -Z, appears up on the screen and +Z near side appears down). Then camera right = forward × up? Standard: right = normalize(cross(forward, up))? For right-handed, right = cross(forward, up) gives... forward=(0,-1,0), up=(0,0,-1): cross = ((-1)(-1) - 0*0, 0*0 - 0*(-1), 0 - (-1)*0) → let me compute properly: cross(a,b) = (a_y b_z - a_z b_y, a_z b_x - a_x b_z, a_x b_y - a_y b_x). a=(0,-1,0), b=(0,0,-1): x = (-1)(-1) - (0)(0) = 1; y = (0)(0) - (0)(-1) = 0; z = 0*0 - (-1)*0 = 0. So right = +X. Good. So screen: right = +X, up = -Z, i.e. +Z appears at bottom of screen.

Clockwise on screen from top-view: bottom (+Z, front) → left(-X)? Clockwise order on screen: top → right → bottom → left → top. In screen terms: up(-Z) → right(+X) → down(+Z) → left(-X). So clockwise: +Z (down) → -X (left). Yes! So U clockwise maps front to left, consistent with the -90° about +Y computed above (front→left). 

So: U = rotate about +Y by -90°? We found R_y(-90) maps (0,0,1)→(-1,0,0), front→left. Yes. So U: axis +Y, angle -π/2. D = opposite = +π/2 about Y (since looking from bottom, clockwise). R: axis +X, R clockwise viewed from +X (right side). Viewed from +X looking toward origin: forward = (-1,0,0), up = (0,1,0)... then right = cross(forward, up) = ? a=(-1,0,0), b=(0,1,0): x = 0*0-0*1 = 0; y = 0*0 - (-1)*0 = 0; z = (-1)(1) - 0 = -1. So right = -Z. Hmm, that means when looking from +X, +Z (front) appears on the left of screen. Wait: looking from the right side of the cube toward the center, the front face (+Z, which was toward the original viewer) is to your... If I stand to the right of the cube and look at it, front face is on my left. Hmm, depends on which way "looking" — I'm at +X looking in -X direction. Up is +Y. My right hand points to -Z? Facing -X with up +Y, right = forward × up computed as above = -Z. Yes so front (+Z) is to my left. Clockwise on screen: top → right → bottom → left: so +Z (left) → +Y (top) → -Z (right) → -Y (bottom). So R clockwise maps front (+Z) → up (+Y). Check physical: right face turned clockwise (viewed from right side) — the front-right edge goes up. Yes, standard R move takes the front-right column up. Actually with F green, R red: R move takes front-right vertical column up? R = clockwise of the right face viewed from the right side. Yes, front → up. Good.

R_y? We need rotation about +X: R_x(θ): y' = y cosθ - z sinθ, z' = y sinθ + z cosθ. For θ=+90°: (0,0,1) → y' = -1, z' = 0 → -Y. For θ=-90°: (0,0,1) → (0, 1, 0) = +Y: front→up. So R = axis +X, angle -π/2. L = opposite: +π/2 about X.

F: clockwise viewed from +Z (front). forward = (0,0,-1), up = (0,1,0), right = cross(forward,up): a=(0,0,-1), b=(0,1,0): x = 0*0 - (-1)(1) = 1; y = (-1)(0) - 0*0 = 0; z = 0*1 - 0*0 = 0 → +X. Good. Clockwise: up(+Y) → right(+X) → down(-Y) → left(-X). So F clockwise maps +Y → +X, i.e. up→right. R_z(θ): x' = x cosθ - y sinθ; y' = x sinθ + y cosθ. θ = -90: (0,1,0) → x' = -y sinθ = -1*(-1) = 1, y' = x sinθ + y cosθ = 0 → (1,0,0) = +X. Yes. So F = axis +Z, angle -π/2. B = +π/2 about Z.

D = axis +Y, +π/2. L = +π/2 about X. B = +π/2 about Z.

Great: U,R,F are -90 about Y,X,Z respectively; D,L,B are +90.

Now the animation: use a pivot Object3D at origin, add the layer cubies (preserving world transforms via THREE's attach()), animate rotation, then on complete, restore by detaching back to a cubies container and snapping to grid.

Note: For 90° multiples, positions after rotation are integer coordinates and rotations are axis-aligned, so snapping via rounding position and re-orthogonalizing the quaternion/matrix is straightforward.

State tracking: maintain for each cubie: id, home position, and current position (Vector3 with components in {-1,0,1}) and orientation (rotation matrix snapped). Stickers: for each sticker mesh, store its face normal (in cubie local space) and color; when computing logical state, compute world normal = cubieQuaternion * localNormal and world position; find which face/color.

I'll write a function `getStateSignature()` returning e.g. a string of 54 facelets: for each face in order U,D,F,B,R,L, for each of 9 positions, the color of the sticker whose outward normal matches the face direction and whose position matches the grid slot. That lets me verify move + inverse = same arrangement (compare with initial signature).

For verification in-browser: I can expose `window.__cube` API and use the browser tool to run JS? The browser tool actions: reload, inspect, screenshot, motion, click, drag, key, type, scroll. There's no "evaluate JS" action listed. Hmm. So verification must be through DOM/console inspection and screenshots. I can log things to console — but inspect shows console? Let me check what "inspect" returns: presumably DOM + console messages. I can use `read` of console via inspect. Also I could add a status panel in the DOM that reflects state, e.g. show a text line with the signature hash or "SOLVED"/state. That would help verification via DOM inspection. Good idea: add a hidden-ish dev readout element with id="stateDump" containing the facelet signature. Actually keep a small "status" line showing move count and whether solved. Plus data attributes on buttons.

Alternatively I can test the core cube logic in Node by extracting the JS? Since three.min.js is present and exports for CommonJS (`typeof exports == 'object'`), I can require it in Node and run headless logic tests by evaluating my index.html script with a stub DOM. That's more work. Simpler: do logic test in node with a jsdom-ish stub? Might not have jsdom. Let me check node_modules for jsdom/puppeteer.

Actually the browser tool exists, so presumably a browser is available. Let me first write the file, then use the browser tool: click buttons, screenshot, inspect DOM (read the facelet signature text displayed in DOM). I'll add a "verify" element that displays a compact state string; that makes DOM-based verification easy.

Design layout: canvas full screen; panel with buttons (bottom or side); header title. Nice styling with gradients, rounded buttons, hover, active. Disable buttons while animating (add .disabled and set aria-disabled). Queue: allow clicking during animation to queue up to some moves — simpler: disable during animation but also implement a queue (accept clicks, queue them, run sequentially). I'll do a queue with max length.

Also add keyboard shortcuts: u d l r f b with shift for prime.

Let me check three.min.js version for API compatibility (r132-ish uses Geometry removed, BoxGeometry with groups, PlaneBufferGeometry removed in r13x?). Let's check quickly.

r128. So `THREE.sRGBEncoding` exists (number), `outputEncoding` on renderer exists in r128. BoxGeometry has groups (material index array). Good.

Note in r128, `PlaneGeometry` exists. `MeshStandardMaterial` fine. Lights: use DirectionalLight + AmbientLight + HemisphereLight.

Let me now write index.html.

Structure:

```html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<title>Rubik's Cube 3D</title>
<style>...</style>
</head>
<body>
<div id="app">
  <canvas? no — renderer appends canvas to #stage>
  <div id="stage"></div>
  <header>...</header>
  <div id="hud">...</div>
  <div id="panel">buttons</div>
</div>
<script src="three.min.js"></script>
<script>...</script>
</body>
</html>
```

Cube construction:
- cubieSize = 1, gap = 0.02? Standard: positions -1,0,1 spacing 1; cube body is BoxGeometry(0.97,0.97,0.97) dark plastic; stickers are PlaneGeometry(0.86,0.86) placed at distance 0.5 from center on each outward face (0.5 > 0.485 half of body, so sticker floats above surface). Actually place sticker at 0.5 offset along normal while body half-size = 0.485 → 0.015 gap. Also round corners visually? Keep simple.

Better visual: use a body with slightly rounded look is complex; skip.

Sticker material: MeshLambertMaterial? In r128, MeshStandardMaterial with roughness .35, metalness 0. Add slight emissive to keep colors vivid. Use MeshPhongMaterial for punchy specular.

Body material: single shared MeshStandardMaterial dark (#111) roughness .6.

Only create stickers for outer faces (where coordinate == ±1 component).

Cubie object: THREE.Group per cubie containing meshes. Actually simpler: each cubie is a THREE.Mesh (body) with sticker children (Mesh). Group not needed. Use mesh with userData {stickers: []}.

Layer selection: current positions snapped to integers; select those with round(pos[axis]) === layerIndex (-1,0,1).

Move animation:
```
function beginMove(move) {
  // move = {axis:'x'|'y'|'z', layer:-1|0|1, angle: ±PI/2}
  pivot.rotation set from ... use pivot with quaternion
  cubies.forEach(c => if selected pivot.attach? )
}
```
Careful: pivot must be a child of the same parent (cubeRoot) at origin. Since cubeRoot will be identity at origin (I'll keep the whole cube group static and orbit the camera instead), the pivot can be added to cubeRoot. Use `pivot.attach(cubie)` to preserve world transform. After animation completes: set pivot.rotation to exact final, updateMatrixWorld, then for each child `cubeRoot.attach(child)`, then snap.

Snapping: position round each component to integer (values near -1,0,1 with possible ±0 tolerance). Rotation: decompose quaternion → matrix → snap each element to nearest of {-1,0,1} → build new quaternion from snapped rotation matrix. Since rotations are multiples of 90°, exact.

Implementation of snap:
```
function snapCubie(c){
  c.position.set(Math.round(c.position.x), Math.round(c.position.y), Math.round(c.position.z));
  const m = new THREE.Matrix4().makeRotationFromQuaternion(c.quaternion);
  const e = m.elements;
  for(let i=0;i<16;i++) e[i] = Math.round(e[i]);
  // build matrix3
  const nm = new THREE.Matrix4(e[0],e[1],e[2],0, e[4],e[5],e[6],0, e[8],e[9],e[10],0, 0,0,0,1);
  // hmm Matrix4 constructor takes row-major args
```
THREE.Matrix4 constructor: elements passed in row-major order: set(n11,n12,n13,n14, n21,...). And `elements` is column-major. Easier: create Matrix4, set elements directly from rounded values (column-major), then `quaternion.setFromRotationMatrix(m)`.

So: round all 12 rotation elements (indices 0..2, 4..6, 8..10) and set 3,7,11,15 appropriately = 0,0,0,1. Then `c.quaternion.setFromRotationMatrix(m)`. Good, rounding to nearest integer works since values are ~ -1,0,1 within float error.

State signature: iterate stickers; each sticker has local normal (fixed at creation) — the sticker is a child of the cubie, so world normal = cubie quaternion applied to local normal (plus any parent rotations, but parents are cubeRoot identity). Compute rounded world normal vector (nx,ny,nz). Position: world position of sticker = cubie.position + localNormal*0.5; take the two nonzero coords... Actually to find the facelet slot: face direction = world normal; then within the face, coordinates determined by the other two axes of the sticker's world position (round the cubie position components).

Build map: for face in FACES order (U:+Y, D:-Y, F:+Z, B:-Z, R:+X, L:-X), define slot ordering by two axis directions, produce 9 chars each (color letter). Signature string of 54 letters. Compare against solved signature (center stickers define the color per face).

Also for verification I want a DOM readout: `#stateOut` textContent = signature (small monospace, maybe in a details panel). I'll include a "State" line in the HUD showing solved/not solved and the facelet string in a `<code>` element (title attribute). Keep it subtle visually. Maybe put in a collapsible <details> at bottom-left "state readout". That's fine visually.

Facelet ordering for signature (standard-ish):
For U face (normal +Y): rows by z from -1 (back) to +1 (front)? Let's define: for each face, use (a,b) where a = horizontal axis, b = vertical axis, and index = row*b_axis... Just define per face:
- U (+Y): horizontal = +X (col), vertical = -Z (row) → reading top layer = back row.
- D (-Y): horizontal = +X (col), vertical = +Z.
- F (+Z): horizontal = +X, vertical = +Y (top row first → y from +1 to -1).
- B (-Z): horizontal = -X, vertical = +Y.
- R (+X): horizontal = +Z, vertical = +Y.
- L (-X): horizontal = -Z, vertical = +Y.

For each face, iterate rows in order given by vertical axis from -1..+1 mapped... Let me define simply: for face f, colAxis (a vector), rowAxis (vector). For r in 0..2, for c in 0..2: pos = center + (r-1)*rowAxis + (c-1)*colAxis (in grid units). Then find the sticker whose cubie position equals that grid coordinate and whose world normal equals face normal. Store color char.

To compute: build a dict keyed by `${x},${y},${z},${nx},${ny},${nz}` → color char. Then for each face and slot, look up. If any missing → invalid.

Determining rowAxis/colAxis vectors as integer triples:
- U: normal (0,1,0), rowAxis: from r=0 (top) to r=2, want top = back = -Z → rowAxis = (0,0,-1)?? pos = center + (r-1)*rowAxis: r=0 → offset = -rowAxis = (0,0,1) = +Z (front). That's wrong; we want r=0 at back (-Z). So set rowAxis = (0,0,1) giving r=0 → offset -(0,0,1)=(0,0,-1) back. Hmm confusing. Let's just define rowAxis as direction of increasing r: for U, increasing r goes from back to front → rowAxis = +Z. colAxis increasing c = +X. Fine; exact ordering doesn't matter as long as deterministic. So:
- U: row=+Z, col=+X
- D: row=-Z, col=+X
- F: row=-Y, col=+X
- B: row=-Y, col=-X
- R: row=-Y, col=+Z
- L: row=-Y, col=-Z
All rows/cols pass through center of the face at the normal coordinate ±1.

Center stickers: the center piece of each face. Solved signature has each face's 9 chars equal to its own color.

Scramble: generate 20-25 random moves avoiding immediate same-axis repeats, enqueue them. Use the same move pipeline.

Reset: restore solved state: rebuild cubies' positions/quaternions to home. Simplest robust: keep each cubie's home position and identity quaternion; on reset set them directly (and remove stickers? no). Since I store home position per cubie, reset = for each cubie: position.copy(home); quaternion.identity(). Then re-attach all cubies to cubeRoot (in case a move is in flight — block reset during animation or cancel: I'll disable during animation; simpler to allow reset anytime after finishing current animation; if animating, set a pendingReset flag). Also reset camera (orbit target = origin, spherical to initial). Also clear queue, reset move counter/timer.

Camera orbit controls (custom):
- spherical: radius (default 12?), theta (azimuth), phi (polar). Initial: theta = 0.65π?? Let's compute so that we see U, F, R: place camera at (5.2, 5.2, 6.5)-ish normalized *radius. Use radius 11, phi (from +Y) = 1.05 rad (~60°), theta = π/4 (45°, gives camera toward +X+Z). Position = target + radius*(sin(phi) sin(theta), cos(phi), sin(phi) cos(theta)). With theta=π/4: x = r sinφ * .707, z = r sinφ * .707 → front-right-top. Good. Cube fully visible: cube half-diagonal ≈ √3 ≈ 1.73 units, plus we have spacing 1 → cubie positions ±1 with size 1 → half extent 1.5, half-diagonal ≈ 2.6. Camera fov 45 at distance 11 → visible half-height at target = 11*tan(22.5°) = 4.56 > 2.6. Fully visible. Good.

Also make cube group rotate? No — cube static, camera orbits (as spec says dragging background orbits camera).

Zoom: wheel adjusts radius clamped [7, 22]. Also handle touch: pointer events unify. Add touch support: single-finger drag = orbit/turn; two-finger pinch = zoom. Keep modest: implement pinch zoom with two pointers.

Aspect/responsive: fit camera distance to canvas aspect so cube fully visible initially — I'll compute base radius from aspect: radius = fitRadius(targetHalf=2.9, fov) considering both vertical and horizontal FOV. And zoom bounds relative.

Drag-to-turn logic:
On pointerdown: raycast against cubie meshes (bodies + stickers). If hit → mode 'turn', record hitPoint (world), hitFaceNormal (world, from the sticker/cubie face), start pixel. On pointermove beyond threshold (10px): compute drag vector in world: I'll project a 3D delta: take hitPoint and compute point on the face plane under current pointer via ray-plane intersection; dragWorld = p_now - p_hit. Then express dragWorld in cube axes (already axis-aligned since face plane is axis-aligned): find the cube axis (of the two in-plane axes) with the larger |dot| → inPlaneAxis. Rotation axis = faceNormal × inPlaneAxis (integer cross) — direction sign: rotating the layer about axis A by +90° moves faceNormal... let's derive: we want the drag to move the surface point along dragWorld direction. The rotation axis for the layer: axis = cross(faceNormal, dragDir) (unit). Velocity of point = ω × r, where r ≈ point position, ω = axis * ω. At a point on the face with position p ≈ faceNormal * 1 + tangential, velocity = ω × p. For a point at the face center p = faceNormal: velocity = axis*ω × faceNormal. We want that ∝ dragDir. cross(axis, faceNormal) = dragDir → axis = ?

Using identity: if axis = cross(dragDir, faceNormal) then cross(axis, faceNormal) = (dragDir×faceNormal)×faceNormal = faceNormal*(dragDir·faceNormal) - dragDir*(faceNormal·faceNormal) = -dragDir (since dragDir ⟂ faceNormal, |faceNormal|=1). So cross(axis, faceNormal) = -dragDir. We want +dragDir → axis = cross(faceNormal, dragDir). Check: cross(faceNormal, dragDir) → cross(that, faceNormal) = (faceNormal×dragDir)×faceNormal = dragDir*(faceNormal·faceNormal) - faceNormal*(...) hmm use (a×b)×c = b(a·c) - a(b·c): with a=faceNormal,b=dragDir,c=faceNormal: = dragDir*(faceNormal·faceNormal) - faceNormal*(dragDir·faceNormal) = dragDir. Yes. So axis = cross(faceNormal, dragDir), positive rotation about that axis moves the face along dragDir. 

Now map axis to one of ±X, ±Y, ±Z; then determine move: rotation about +axisDir by +90° is equivalent to rotation about -axisDir by -90°(i.e., the inverse). Compute angle sign so that we rotate about the canonical positive axis with angle ±90: if axis = +X, angle=+90; if axis=-X, angle=-90 about +X. Layer = sign of the faceNormal's component along the axis. Then which notation move does it correspond to? We can just execute a generic move {axis, layer, angle}; but to display the name (e.g., "R'"), map:
- axis Y, layer +1: angle -90 = U, +90 = U'
- axis Y, layer -1: +90 = D, -90 = D'
- axis X, layer +1: -90 = R, +90 = R'
- axis X, layer -1: +90 = L, -90 = L'
- axis Z, layer +1: -90 = F, +90 = F'
- axis Z, layer -1: +90 = B, -90 = B'

Layer index: from faceNormal component along axis = ±1 → layer = that sign * ... For a face with normal +Y and axis Y, the layer is the +1 layer. Yes, layer = sign(faceNormal · axisUnit).

Good. So drag turning yields a named move that we enqueue (animating). I'll do the animation after the pointerup? Better: animate on crossing threshold immediately (with pointer still possibly moving), and lock subsequent drags until done. Simplest: when threshold crossed, compute move, enqueue it, and mark this gesture as consumed (further moves in same gesture ignored). Fine.

If the pointerdown hits the cube but the drag ends up mostly perpendicular to the face (out of plane, e.g., dragging toward the camera), skip.

Also add: clicking on cube without drag → nothing (no turn).

Renderer: antialias true, pixelRatio min(devicePixelRatio,2), outputEncoding sRGB, tone mapping? keep default but set colors accordingly. Add shadow? Skip shadows for simplicity/perf, use lighting for shading: hemisphere + 3 directional lights for face distinction. Note: with distinct directional lights the face colors may look uneven. Use: AmbientLight(0xffffff, 0.55) + DirectionalLight(0xffffff,0.45) at (5,10,7) + DirectionalLight(0.25) at (-6,-4,-8). Fine.

Background: CSS gradient behind transparent canvas (alpha:true). Nice look.

Now HUD: title, move count, timer, "Solved / Not solved" badge, hint text. Buttons: grid of 12 turn buttons labeled U U′ D D′ L L′ R R′ F F′ B B′, plus Scramble / Reset. Maybe grouped in two rows per face pair. Add keyboard hints.

Also indicate "locked" state: panel dim + cursor progress.

Let me also handle window resize.

Let's write the code.

Animation loop: requestAnimationFrame always running (render). Move animation uses elapsed time, easing (easeInOutQuad). Duration 260ms; scramble moves maybe shorter (160ms).

Queue: array of move descriptors; if not animating, start next.

Also add a small "history" display of recent moves.

Let me write index.html now.

For stickers: I'll make sticker geometry with a slightly rounded square via ShapeGeometry? Could use THREE.Shape with rounded corners and ShapeGeometry — supported in r128 (ShapeGeometry exists). Rounded sticker looks great. But UV/lighting fine. Let's do it: rounded rect shape, centered, size 0.82, radius 0.12, then ShapeGeometry, then rotate/position as needed. ShapeGeometry is in XY plane facing +Z; for each face normal, orient by rotating: +Z: none; -Z: rotateY(π); +X: rotateY(π/2); -X: rotateY(-π/2); +Y: rotateX(-π/2); -Y: rotateX(π/2). I'll bake rotation into geometry? Each sticker shares one of 6 geometries created via `geometry.clone().applyMatrix4(...)`. Better: create 6 base geometries (shared) oriented with normal facing outward at origin, then each sticker mesh position = normal * 0.5.

Note ShapeGeometry rounded rect with curveSegments — fine.

Careful: double-sided not needed; front side faces outward.

Let me define function roundedStickerGeo(size, radius) returning geometry in XY plane with normal +Z, then apply rotations for others.

Also I'll store on each sticker userData: localNormal (Vector3, integer), colorChar.

Edge case: ShapeGeometry with hole? no.

Body geometry: BoxGeometry(0.97,0.97,0.97) shared; material dark. Maybe give body a slight bevel look using RoundedBoxGeometry — not available in r128 core. Skip.

Now code. Also add "state readout" <details> with <code id="facelets">.

Let me write it.

```js
const FACES = {
  U: {normal:new THREE.Vector3(0,1,0), color:0xf7f7f7, char:'W', row:[0,0,1], col:[1,0,0]},
  D: {normal:(0,-1,0), color:0xffd500 'Y', row:[0,0,-1], col:[1,0,0]},
  F: {normal:(0,0,1), color:0x00a85a 'G', row:[0,-1,0], col:[1,0,0]},
  B: {normal:(0,0,-1), color:0x0057d0 'B', row:[0,-1,0], col:[-1,0,0]},
  R: {normal:(1,0,0), color:0xe4322a 'R', row:[0,-1,0], col:[0,0,1]},
  L: {normal:(-1,0,0), color:0xff7a1a 'O', row:[0,-1,0], col:[0,0,-1]},
};
```
Move definitions:
```js
const MOVES = {
  "U": {axis:'y', layer:1, angle:-Math.PI/2},  "U'":{axis:'y',layer:1,angle:Math.PI/2},
  "D": {axis:'y',layer:-1,angle:Math.PI/2}, "D'":{...,-Math.PI/2},
  "R": {axis:'x',layer:1,angle:-Math.PI/2}, "R'":{...,+},
  "L": {axis:'x',layer:-1,angle:Math.PI/2}, "L'":...-
  "F": {axis:'z',layer:1,angle:-Math.PI/2}, "F'":...,
  "B": {axis:'z',layer:-1,angle:Math.PI/2}, "B'":...,
};
```

Wait: careful for L and B and D: for D, rotation about +Y by +90 (we said D = +π/2 about Y). But note the layer for D is the -1 layer; rotation about +Y by +90 of the bottom layer viewed from below (+Y axis direction pointing away from viewer at bottom → clockwise viewed from -Y = rotation about -Y by -90 = about +Y by +90)... hmm let me redo: "D clockwise viewed from below (from -Y)". Rotation that is clockwise when viewed from -Y equals counterclockwise when viewed from +Y, which equals positive rotation about +Y? Positive rotation about +Y is counterclockwise viewed from +Y (right-hand rule). Viewed from -Y it's clockwise. Hmm: right-hand rule about +Y: thumb +Y, fingers curl counterclockwise as seen from the +Y end looking back at origin (i.e. viewing down -Y direction). So positive about +Y is CCW when viewed from above, CW when viewed from below. D is CW from below → positive about +Y = +90. ✓. Similarly L (CW from -X) = positive about -X? CW viewed from -X = CCW viewed from +X = positive about +X = +90. ✓ matches. B (CW from -Z) = CCW from +Z = +90 about Z ✓.

Great.

Now let's verify cycle correctness mentally for U: {y,1,-90}: front-top row → left. ✓ standard.

For R {x,1,-90}: front-right col → up ✓.

Now let's implement.

Additional verification thought: also verify stickers move with cubies (they're children, yes).

Let me write the file now. I'll aim for clean, complete code.

For the timer: start on first move after scramble, stop when solved. Optional nicety.

Code:

```html
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Rubik's Cube — 3D</title>
<style>
:root{
  --bg1:#0b1220; --bg2:#16203a; --panel:rgba(18,24,40,.78); --line:rgba(255,255,255,.12);
  --text:#e8edf7; --muted:#93a2bd; --accent:#5ad1ff;
}
*{box-sizing:border-box}
html,body{height:100%;margin:0}
body{font-family:...; color:var(--text); background: radial-gradient(...)}
#stage{position:fixed;inset:0}
canvas{display:block;outline:none}
...
</style>
```

Panel layout: bottom center, with groups. Use flex/grid. Responsive: on small screens, buttons wrap, panel scrolls.

I'll write it now with care.

Also pointer handling: use `pointerdown` on the stage element; `setPointerCapture`.

Let's produce the file.

One more: "bounded wheel zoom" — clamp radius to [minRadius, maxRadius] where minRadius = fitRadius*0.55, maxRadius = fitRadius*2.2. And prevent page scroll (preventDefault on wheel with passive:false).

fitRadius: compute needed radius so cube (bounding sphere r≈2.75 with margin) fits: vertical fov: rv = boundingR / sin(fovV/2) roughly; use distance = boundingR / tan(fovV/2) * 1.15, and horizontal: fovH = 2*atan(tan(fovV/2)*aspect) → distance_h = boundingR/tan(fovH/2)*1.15; radius = max(v,h). Cap min 6.

Camera near/far: 0.1, 100.

Initial camera: also store initial spherical (theta, phi) for reset and recompute radius on resize for reset. On reset, set radius to fit radius.

Note: on resize, keep radius but ensure not smaller than fit? If window shrinks, cube could overflow. I'll recompute fitRadius and scale radius proportionally when the fit changes? Simpler: on resize, recompute minRadius = fitRadius, and clamp radius ≥ fitRadius*0.98... Hmm but zoom bounds allow radius smaller than fit (user zooming in). Requirement: "Keep the cube fully visible initially and support bounded wheel zoom" — zooming in partially is fine as long as bounded. I'll allow zoom in to fitRadius*0.6. On resize, if in 'auto' state (user hasn't zoomed), set radius = fitRadius. Track userZoomed flag; reset clears it. Good.

Let's write.

Also add a subtle ground reflection? no. Add a faint glow behind cube via CSS radial gradient. Fine.

Let me write the whole thing.

Move animation function:

```js
let anim = null; // {name, axisVec, cubies, pivot, duration, elapsed, dir}
function startMove(name){
  if(anim) { if(queue.length<40) queue.push(name); return; }
  const mv = MOVES[name]; ...
}
function tickAnim(dt){
  anim.elapsed += dt;
  const t = Math.min(1, anim.elapsed/anim.duration);
  const e = easeInOut(t);
  pivot.rotation[axis] = anim.dir * e;   // where dir = ±PI/2 as target angle
  if(t>=1){ finishMove(); }
}
```
Pivot rotation: create pivot Object3D added to cubeRoot; set pivot.rotation[axis] = angle each frame; cubeRoot.updateMatrixWorld(true) needed — render loop will do it.

finishMove: set exact angle, updateMatrixWorld, then for each child slice → cubeRoot.attach(child), snap; remove pivot; push history, update counters, check solved; then process queue.

attach: `cubeRoot.attach(o)` — in r128 Object3D.attach exists (yes, since r84). Also `pivot.attach(c)`.

Need pivot.matrixWorld updated before attaching children at start? At start we do pivot.attach(c) which uses pivot's matrixWorld; pivot is at origin with identity rotation initially → fine, but matrixWorld must be current. Since pivot just added to cubeRoot, call cubeRoot.updateMatrixWorld(true) after adding pivot. Then attach. Then set rotation.

Actually order: add pivot to cubeRoot; cubeRoot.updateMatrixWorld(true) (pivot.matrixWorld identity); attach cubies (their world matrix preserved, becomes relative to pivot); animate; on finish set final rotation, updateMatrixWorld(true), detach each child via cubeRoot.attach(child), snap.

Now state signature function: iterate cubies; for each sticker: worldNormal = localNormal.clone().applyQuaternion(cubie.quaternion) (parent chain identity rotation since cubeRoot not rotated — I'll keep cubeRoot unrotated; safe: instead use `cubie.getWorldQuaternion`), then round. worldPos = cubie.getWorldPosition; then facelet key.

Build dict and read out; also compare against expected center colors to decide solved: solved if for each face, all 9 chars equal face's own char.

Alright — write the code.

Also keyboard: keydown handler mapping letters; shift → prime. Also 's' scramble, 'r' reset? 'r' conflicts with R move. Use 'Escape' for reset? I'll add: keydown for u,d,l,r,f,b (+shift), '1' scramble? Just document: Space = scramble? Space may scroll but preventDefault. Use 'S' for scramble and 'Backspace'/'Delete'? I'll set: keys u d l r f b with Shift for inverse; 'Enter' = scramble? Let's do: 'x' or 'S' → scramble (shift+s?), and '0' → reset. Document in hint: "S = scramble, 0 = reset".

Now write the file.

I'll also add a move counter and current-move flash on the corresponding button.

Time to write.

Now let me test in the browser. Also I should verify the move-sign convention programmatically. Let me first run a Node test of the state logic by extracting the script and stubbing THREE-independent parts? Actually the logic uses THREE which is available in Node via require. But the DOM parts would fail. Alternative: verify via the browser DOM readout using the debug panel (facelets element) and inspect action.

Let me check whether the browser tool can read text content — "inspect" presumably returns DOM info. Let's try.

Also I want a headless test of move correctness. I could write a small node script that reimplements the signature function using only the parts that need THREE — actually I can extract the pure functions (FACES, MOVES, facelets over an abstract cubie model) and test with THREE in node. Let me write a node test that mirrors the logic:

- Build 27 cubies with position + quaternion + stickers (local normals + chars).
- Apply move: rotate selected about axis by angle.
- Snap.
- Compute facelets.
- Test: U then U' returns to solved; U^4 = solved; check the U cycle gives the correct facelet permutation (e.g., after U, the F face's top row should be the R face's top row? Let's determine: U clockwise moves front top row to left top row, so the facelets arriving on F's top row come from R's top row. In standard: U: F→L, L→B, B→R, R→F. So after U, F's top row contains R's former top row color (R = red 'R'), and R's top row contains B's (blue).

Let me write the node test replicating the code. To avoid code duplication risk, I can extract the script from index.html and run parts? Simplest: write a standalone test file that copies the core logic (same math, same snapping) and asserts. Duplication in test is acceptable.

Actually better: make the test load index.html's script text and evaluate it in a sandbox with a fake DOM. The script does lots of DOM stuff... I could build a minimal fake document/window/renderer stub. WebGLRenderer creation would fail in node (no canvas/WebGL). Hmm.

Alternative: check if there's headless chrome available with puppeteer in node_modules. Let me check.

The facelet lookup is broken (all '?') — bug in my key building. In the test: `map` key uses p+nr as slot position: For a sticker on cubie at position p with world normal nr, the facelet slot it occupies is... The outward face of the cube is at coordinate ±1 along the normal axis. The cubie position p is in {-1,0,1}. The slot on the face: the position where that sticker sits is p + nr? Hmm: for a cubie at (1,1,1) with normal (0,1,0) (U face), the sticker's slot on the U face should be grid coords (1,1,1) → but the U face layer is y=1, and within that face the slot is determined by x and z. Using slot key = p + nr gives (1,2,1) — and in the lookup, for face U, p = F.n = (0,1,0) plus (r-1)*row + (q-1)*col which ranges x,z in {-1,0,1}, y = 1. So lookup key positions have y=1 while map keys have y=2. Mismatch! That's the bug — also present in index.html.

Fix: the slot position should just be p (the cubie position) plus the normal direction encoded implicitly by the face. The correct key: normalize so that the axis along the normal is set to the face's coordinate (±1) rather than ±2. So define slot = p, but only valid when p·n === 1 (i.e., p has the component matching normal direction = 1). Since p is in {-1,0,1}, cubie positions on the U face have y=1, matching F.n=(0,1,0) exactly in that component. So key should just be [p, nr] without adding. Let me fix: map key = [px,py,pz,nx,ny,nz].join(',') and lookup uses p (with p = F.n + offsets) and nn = F.n. For U face slot at x=1,z=1: p=(1,1,1); and the map entry for cubie (1,1,1) sticker normal (0,1,0) key = "1,1,1,0,1,0". Lookup key = "1,1,1,0,1,0". ✓ matches.

But wait: is p·n == 1 guaranteed? For cubie at position (1,1,1) with sticker normal (0,1,0): p·n = 1 ✓. After moves, a cubie with a U-facing sticker always has y=1 (since outward-facing stickers are on the outer layer). Yes — a sticker whose world normal is +Y must be on a cubie with y=1 because the sticker's local normal is attached to the cubie's outer face, and the original outer faces are the only stickers. ✓

So fix in index.html: remove the `+ nx` additions. Let me re-test.

Also in facelets() in index.html I wrote `map[[px + nx, py + ny, pz + nz, nx, ny, nz]...]`. Change to `[px, py, pz, nx, ny, nz]`.

Let me re-run the node test with the fix, and also verify cycle correctness (U sends F top row → L etc.).

0 stickers: my cubie sticker creation condition is wrong. `x*f.n[0]===1 && y*f.n[1]===1 && z*f.n[2]===1` — for a cubie at (1,1,1) and face U (n=(0,1,0)): x*0=0, y*1=1, z*0=0 → requires all three ===1, which fails. Should be: the components where n is nonzero equal n (i.e., p·n === 1). Fix: `x*f.n[0]+y*f.n[1]+z*f.n[2] === 1`. Same bug in index.html! Let me check index.html: 

```
var cx = x * f.n[0], cy = y * f.n[1], cz = z * f.n[2];
if (cx === 1 && cy === 1 && cz === 1) {
```
Yes — same bug. Must fix to `cx + cy + cz === 1`.

Let me fix both.

The move convention is correct: U sends F→L→B→R→F (standard U: front top row goes to left face — here the left top row shows GGG which was F's color ✓, and F's top row now shows RRR ✓).

Wait check: standard U cycle is F→L, L→B, B→R, R→F. After U, F's top row = R's old top row (red) ✓ consistent with R→F. And L top = GGG (F→L) ✓. 

Now let me add more tests: each move + inverse restores; each move^4 = solved; a sexy move (R U R' U') x6 = solved; random scrambles keep 54 stickers with valid permutations (only color-legal states: centers fixed, each face has 9 stickers of... well check center invariant and count of each color = 9).

Also verify reset restores.

Then update index.html fixes:
1. Sticker attach condition bug (cx===1&&cy===1&&cz===1) → sum === 1.
2. facelets map key: drop the +n addition.

Let me write a fuller test in the same harness.

The reset2 uses c.home which was set after reset2 call... Actually the error is at line 37 in facelets: dup key? Let me see the error message. Line 64 is in NAMES.forEach inverse tests: `reset2(); ...` — c.home was set at line ~62 after reset2 was defined but the loop calls reset2 before... no, home assignment happens before the forEach. Hmm but the error trace: at facelets line 37 (dup) called from line 64.

Issue: my inverse test used `apply(n==="U"?"U'": n.replace("'",''))` nonsense — I applied the move and then applied something wrong (e.g. for n="D'", replace gives "D" then inv = "D" again) — applying non-inverse moves twice may put two stickers in the same slot? No, that can't create dup keys since it's still a legal state...

Wait, line 64 might be the "order-4" or the "dup" could arise if snapping broke. Let me print the actual error message.

My sloppy test: I applied move n then applied an extra wrong move, so the state got 3 turns total not cancelling... but dup key `0,0,0,0,-1,0` means two stickers claiming the same slot: the core cubie (0,0,0) has no stickers... unless a corner/edge cubie moved into the center position. That indicates the *test's* move application is wrong for the middle layer: e.g. applying the "D'" after "D"? No, positions: layer selection uses Math.round(pos.y) === -1. If a cubie at y=0 gets rotated... hmm dup means two cubies ended at same position with same normal — meaning layer selection picked different sets.

Actually the bug is my test line: `apply(n==="U"?"U'": n.replace("'",''))` — for n="U": applies "U" then "U'" then inv="U'" → net U' ≠ dup. Duplicates shouldn't happen from legal moves regardless. Unless snapping corrupted.

Let me look: my earlier line `cubies.forEach(c=>{c.pos.copy(new T.Vector3(0,0,0));});` at the end of the first part (line ~58) moved ALL cubies to (0,0,0)! Then I set home from the corrupted positions and reset2 restores all to 0,0,0 → dups. Yes, that leftover line from the first draft. Remove it and the home capture ordering issue. Let me rewrite the test cleanly.

All logic tests pass: notation convention correct, snapping preserves state, inverse restores exactly, order-4 identity, sexy move ^6 solves, random scrambles stay legal (centers fixed, 9 of each color, no missing facelets).

Now fix the two bugs in index.html:
1. sticker attach condition: `cx === 1 && cy === 1 && cz === 1` → `cx + cy + cz === 1`.
2. facelets map key: remove the +n.

Also review other issues:
- `hit.object.parent.userData.cubie` — stickers' parent is the body mesh, which has userData.cubie ✓. But raycasting against the body itself: hit.object is the body, and `hit.object.userData.kind === 'body'`, parent is cubeRoot (no cubie userData) → my check `hit.object.parent.userData.cubie` fails for direct body hits. The body's own userData.cubie exists. Let me restructure: determine cubieMesh = hit.object.userData.kind === 'sticker' ? hit.object.parent : hit.object. Then check cubieMesh.userData.cubie.

- Body hit normals: hit.face.normal is in object local space for the body mesh; I wrote `.applyQuaternion(cubieMesh.quaternion.clone().invert())` which is wrong direction — for a body hit, the world normal = local normal applyQuaternion(world quaternion). Let me fix: world normal = hit.face.normal.clone().applyQuaternion(worldQuat). Actually I want the *world* face normal, and the local one for the plane. I only use gesture.normal as a world-space normal for the plane. So for a sticker: sticker's local normal userData.n rotated by cubie's world quaternion → world normal. For body: hit.face.normal (local) rotated by cubie world quaternion → world. Both should use getWorldQuaternion. Let me implement properly.

- Also intersectObjects with cubeRoot.children includes sticker meshes (children recursive) ✓.

- `d = p.sub(gesture.point)` mutates p; fine.

- The plane: `new THREE.Plane().setFromNormalAndCoplanarPoint(n, gesture.point)` — n must be unit length ✓ (normalizeInt gives unit axis vector).

- normalizeInt for sign of zero components: if v components are e.g. (0,0,-1) → returns (0,0,-1) ✓. If x=0,y=0,z=0 returns (0,0,0)? First branch: |0|>=|0| && |0|>=|0| true → returns x>0?1:-1 → (−1,0,0) for zero vector. Then guarded by `if (drag.x===0&&...)` never true. Add guard earlier: if d.length()<0.12 return null, so zero vector unlikely. But for the normal case, normal is never zero ✓. Let me make normalizeInt return zero vector if all rounded are 0, and check.

- gesture.x is used for orbit deltas but for the turn gesture I compare against original x/y for threshold ✓.

- `else gesture.x = gesture.x;` — pointless line; remove and instead keep checking on later moves. But note the threshold check uses gesture.x/y as start point (never updated in turn mode) so accumulated delta is used ✓. So remove that else branch.

- finishTurn: `if (!timing && !isSolved()) timing = true;` — starts the clock. OK.

- `render()` in the code is my UI-update function name, but it's also easy to confuse with renderer.render — fine, but note `render()` is called inside loop? No, loop calls renderer.render. UI render() is called on moves/resize. But the clock text updates each frame in loop directly ✓.

- In `render()`, elHist mapping: `history.slice(-16).map(...)` with direction:rtl on the container and joined string... I set CSS direction rtl so the tail is visible. With rtl, spaces may misplace. Simpler: keep last 16 and set direction ltr with overflow hidden? Let's just show the last N moves and let rtl handle truncation; but rtl with the string may reorder punctuation oddly for primes ( ' ). Hmm, `'` in rtl context can flip. Safer: display last ~14 moves without rtl, i.e. `direction:rtl` removed, and rely on flex shrink with text-overflow ellipsis (shows the beginning, hides the end) — I'd rather show the end. Alternative: reverse the string? Let me instead build the history as spans and use rtl with unicode-bidi: plaintext... Simplest robust approach: keep the strip as a fixed-width window showing the last 12 moves, using `justify-content:flex-end; overflow:hidden; white-space:nowrap;` with direction:ltr and putting the moves in a child element that's aligned right. Let me restructure: `<span class="moves"><span id="historyInner">…</span></span>` with .moves{display:flex;justify-content:flex-end;overflow:hidden} and inner white-space:nowrap. That shows the tail. Good, no bidi tricks.

- Prime symbol: MOVES keys use "U'" internally with `'` — the button data-move="U'" ✓ (HTML attribute with single quote inside double quotes ✓).

- Keyboard: `MOVE_NAMES.indexOf(up)` where up is uppercase letter e.g. 'U' ✓; enqueue(up+"'") for shift ✓.

- `key` variable name collision: I declared `var key = new THREE.HemisphereLight(...)` at top-level of IIFE and inside turnFromDrag `var key = ['x','y','z']` (local) — shadowing fine but confusing; also `e.key` usage in keydown — fine. Rename light to hemi to be safe.

- Wheel handler with clamp(e.deltaY,-240,240): deltaMode may be lines (Firefox) giving small values — fine.

- computeFit on resize: logic muddled:
```
var wasFit = fitRadius; computeFit();
if (!userZoomed || cam.radius < minRadius || Math.abs(wasFit-fitRadius)>0.001) { cam.radius = clamp(userZoomed ? cam.radius : fitRadius, minRadius, maxRadius); }
```
Simplify: if (!userZoomed) cam.radius = fitRadius; else cam.radius = clamp(cam.radius, minRadius, maxRadius). computeFit already clamps. Let me clean.

- Initial: computeFit() sets fitRadius then cam.radius = fitRadius.

- PHI initial: CAM0.phi = π*0.32 ≈ 57.6° from +Y → slightly above horizontal, good for seeing U face (since camera y = r cos(57.6°) = 0.53r — above center). Cube center at origin; viewing from above at 57.6° polar means elevation 32.4° → top face visible ✓.

- BOUND = 2.85: half-diagonal of cube with extent 1.5 → √3*1.5 = 2.598. Plus margin → 2.85 ✓. But bounding sphere works only if the cube doesn't rotate — camera orbits, so the sphere is exact ✓.

- fitRadius with fov 45: BOUND/tan(22.5°)=2.85/0.4142=6.88 *1.06 = 7.3 for portrait; for wide screens horizontal fov larger so vertical dominates → radius ~7.3. minRadius=4.0, maxRadius=17.5. At radius 7.3 the cube fills nicely. Good. Actually with alpha:true, background is CSS.

Hmm, careful: at radius = fitRadius exactly, cube touches the frame edges. I multiply by 1.06 for margin. Fine.

- Debug panel position bottom-left overlaps footer? footer is centered; on narrow screens may overlap. Set details.debug left:18px bottom:18px; footer content is centered so slight overlap risk on small screens; hidden below 720px ✓.

- Also make sure buttons disabled while animating (render() sets disabled) but queue still allows via keyboard/drag — that's the "queue" behavior ✓. Requirement satisfied: animate each move and queue or disable further moves.

- Need `render()` called after enqueue to update queue length + disabled state. enqueue → startTurn → sets anim, but render() is called in finishTurn and... startTurn doesn't call render(). Let me call render() at the end of enqueue. And finishTurn calls render() ✓.

- setStatus uses isSolved() each call — fine.

- `flashButton` ✓.

- Scramble logic: messy two-step; simplify to a clean loop that avoids same-axis-same-layer consecutive repeats. Also should avoid 3 repeats of same axis (e.g., U U' D) — not necessary. Let me rewrite:
```
function scramble(n){ var out=[],prev=null;
 while(out.length<n){ var m=MOVE_NAMES[rand]; if(prev && MOVES[prev].axis===MOVES[m].axis && MOVES[prev].layer===MOVES[m].layer) continue; if(prev && MOVES[prev].axis===MOVES[m].axis && out.length>1 && MOVES[out[out.length-2]].axis===MOVES[m].axis) continue; out.push(m); prev=m; }
```
Good: prevents same layer repeats and prevents two consecutive same-axis (slice turns) which are visually confusing. Then enqueue all.

- Scramble durations: use 0.15s for queued moves. In finishTurn I use `queue.length ? 0.15 : 0.26` for the next — good.

- `reset()` while animating: buttons disabled during anim so unlikely, but keyboard could... reset is only via button/key. Since anim guards, let me handle: if anim, cancel animation and bake immediately (my code does partial). Better: bake the current turn instantly (snap positions), then reset. Let me restructure: `cancelAnim()` that finishes the rotation instantly with snapping (reuse code from finishTurn). I'll factor `bake(anim)` used by both finishTurn and reset.

Let me now rewrite the JS sections with these fixes via a fresh full-file write (cleaner than many edits). I'll rewrite index.html entirely with corrections.

Also add: after solving by user (state solved and turnCount>0), show a "Solved 🎉" flash? Keep simple: status shows Solved.

Let me write the final file.

One more consideration: sticker geometry orientation matrices. ROT for +Y: base geometry lies in XY plane facing +Z. To face +Y, rotate about X by -90°: that maps +Z → ? R_x(-90): y' = y cos + z sin(-90)... let's compute using rotation about X by angle θ: (0,0,1) → (0, -sinθ, cosθ). For θ=-90: (0, 1, 0) = +Y ✓. So +Y needs rotateX(-π/2), and -Y needs rotateX(+π/2). I had '0,1,0': makeRotationX(Math.PI/2) → (0,0,1)→(0,-1,0) = -Y ✗. Swap them.

For ±X: rotation about Y by θ: (0,0,1) → (sinθ, 0, cosθ). θ=+90 → (1,0,0)=+X ✓ so +X needs rotateY(+π/2); I had -π/2 ✗. Swap.

Also normals of the geometry after rotation: applyMatrix4 on BufferGeometry transforms normals too ✓ (r128 applies normalMatrix to normals). Yes, `BufferGeometry.applyMatrix4` transforms attributes and normals.

Additionally, ShapeGeometry front face winding: CCW in XY plane → after rotation, still front-facing when viewed from the outward side ✓. But let me double check the shape path is CCW: starting (-h+r,-h) → (h-r,-h) → up right side → left along top → down left side: that's counterclockwise in standard XY ✓ (bottom edge left→right, right edge bottom→top, top right→left, left top→bottom = CCW) ✓. So normals +Z ✓.

Also: ShapeGeometry(s, 6) — the second parameter for ShapeGeometry is curveSegments ✓.

Also verify that sticker rounding with rounded corners looks fine.

Also: the rounded square's normals via computeVertexNormals on a flat shape — ShapeGeometry already generates normals (0,0,1) I think; computeVertexNormals for an indexed plane geometry gives (0,0,1)... Actually ShapeGeometry produces non-indexed? It uses ShapeUtils.triangulateShape; the geometry has normals attribute set? In r128 ShapeGeometry sets normals to (0,0,1) ✓. My computeVertexNormals() call would also compute flat (0,0,1) for the triangulated planar faces — fine either way. Keep computeVertexNormals but note non-uniform triangle splits might average normals to (0,0,1) anyway since all coplanar ✓.

For the +Y face: after applyMatrix4 rotateX(-π/2) the plane faces +Y ✓.

Let me also double check `THREE.PlaneGeometry` unused.

Body material MeshStandardMaterial needs envmap-ish? With lights it's fine.

Now, one risk: performance with 26 cubies × up to 3 stickers = 54 sticker meshes + 26 bodies = 80 draw calls. Fine.

Note the core cubie (0,0,0) has no stickers — include it anyway (invisible, fine) or skip. Keep it but maybe skip adding it to scene to save a draw call. Actually keeping it is harmless; but raycasting could hit the core if a layer is mid-turn... skip core: `if (x===0&&y===0&&z===0) continue;` — cleaner. Then layerOf for middle layers returns 4 cubies (edges+centers) — correct for moves anyway since the core never moves. Do it.

Now write final file.

Camera: also add a subtle floor grid? no.

Let me write.

I need to run the browser now and verify quickly. Note paintUI is called after each move; setStatus in startTurn. Also isSolved() called every frame in loop (when timing) — that's a bit heavy (54 lookups) but fine.

Let me run browser checks: reload, inspect, screenshot, click U, wait, screenshot, click U', check facelets readout returns to solved string.

Cube renders nicely, solved, colors distinct, boundaries visible. Cube slightly large but fully visible? The bottom is cut off by the panel — the cube extends below the visible area? It looks like the cube bottom is hidden behind the control panel, but that's UI overlay, and the cube bottom edge appears around y=730 which is behind panel. Requirement: "Keep the cube fully visible initially". The bottom row is partly obscured by the control pad. I should increase fitRadius margin and/or shift the cube up a bit so it clears the panel.

Quick fix: increase margin factor to ~1.35 and offset camera target slightly up? Better: raise fitRadius multiplier to 1.3 and also lift the cube visually by setting cam.target.y = -0.6 (moves cube up on screen)? Actually target.y negative moves the cube up on screen. Let me instead just increase the fit margin and check.

Time is short (5 min). Let me do the fit change plus verify U + U' facelets.

Change: fitRadius = max(...) * 1.32. Also the debug/hint take space at bottom. Let's do 1.35 and check screenshot.

Also open the facelet readout to verify. Let me batch: edit, reload, then click U (need coordinates: U button ~ (401,641) in 1200x800 viewport per screenshot scale... screenshot is 1200x800 already). Then click U' at (437,641). Then inspect DOM to read facelets? The readout is collapsed; DOM text of #facelets exists regardless — inspect gives visible text only ("FACELET READOUT"). So open details by clicking it (at (84,762)).

Faster: after moves, take screenshot with details open.

Let me do: edit → reload → click details (open) → click U → click U' (queued) → screenshot.

But clicking U' while U animating: button disabled during anim; the click may be ignored. U animation is 0.26s; the click tool happens later, so buttons re-enabled. Fine.

Sequence with separate calls costs time. Do: edit+reload, then click facelet readout, then click U, then inspect (should show facelets scrambled), then click U', then inspect (should show solved string).

Let me combine: click details and click U in one block (independent? second depends on first only for state, both fine in parallel? They're sequential UI actions but no dependency on results). I'll batch them.

Wait, CAM0 phi change to 0.33π is minor; fine.

Also raise the cube a bit: the panel occupies bottom ~230px of 800. With larger radius the cube shrinks. Let me also set cam.target.y = -0.35 so the cube appears higher? That shifts cube up on screen by ~0.35 units. Actually camera looks at target; if target.y is negative, the cube center appears below... camera.position = target + offset, lookAt(target) → cube center is at (0,0,0) which is above target → appears higher on screen. Yes, target.y = -0.5 raises the cube. But orbit rotates around target which is off-center — slight wobble. Keep target at 0 and rely on larger radius. Let's test visually.

Now reload and check.

Still slightly overlapped at the bottom by the history strip. The cube bottom is ~y=730. I need it above ~y=545 (panel top). Options: lift the cube center up on screen by setting cam.target.y negative (e.g., -0.9) and increase radius a bit more. Let's set target.y = -0.75 and factor 1.45. With orbit around target offset, the cube rotates around a point below its center — visually acceptable? It'd make the cube swing. Alternative: use camera offset via `camera.translateY` after lookAt? Simplest robust: keep target at origin but position the whole cubeRoot up: cubeRoot.position.y = 0.9? Then bounding sphere center is above origin; orbiting around origin would swing the cube. Hmm.

Better: shift the projection: camera.setViewOffset to shift the rendered image up. That keeps orbit centered on the cube while moving the cube up on screen. camera.setViewOffset(fullW, fullH, x, y, w, h) with negative y offset shifts view. Let's do: on computeFit, set view offset: camera.setViewOffset(w, h, 0, -h*0.10, w, h)? Offset x=0, y=-0.1h means the sub-rectangle starts above the full canvas → renders content shifted down? Let me think: setViewOffset defines a sub-window of a larger view. full width/height = (w,h), and offset (x,y) is the top-left of the sub-window of size (w,h) within full. If y = -0.1h, the sub-window extends above full → the visible content shifts downward... Actually with y offset increasing, the view moves down (camera looks higher? no). Standard usage: x,y is the offset of the viewport in the full scene; increasing y moves the rendered image up (showing content lower in the full image). Ugh, sign ambiguity — easier: increase radius and reduce panel height? 

Simplest reliable: keep the cube centered in the *free* area above the panel by adjusting cam.target.y. Orbit around a point slightly below the cube center causes the cube to bob slightly when orbiting vertically — acceptable and common. But actually a cleaner fix: make the panel more compact and semi-transparent (it already is translucent, so the cube shows through — the overlap is visually OK but "fully visible" requirement matters).

Given ~4 min left, do: factor 1.5 (smaller cube) and target.y = -0.55 via CAM0 target. Let me implement: cam.target.set(0,-0.5,0) initially and in reset. Then check screenshot.

No python. The sed-like edits: use node.

Note the second replace: the actual source line is
`var cam = { theta: CAM0.theta, phi: CAM0.phi, radius: 11, target: new THREE.Vector3(0, 0, 0) };`
Let me use node with string replacements.

Also careful: target.y=-0.55 means camera looks at a point below cube center → cube appears higher on screen. ✓ (lookAt target below center → center projects above screen center).

Also zoom fit: with target offset, the bounding sphere is centered at origin, not at target, so the fit margin needs to account for the offset: effective bound = BOUND + 0.55. The 1.42 factor gives extra room; check screenshot.

Hmm, the first replace introduced a double space, harmless. Note the `1.34` replacement worked.

Wait, my earlier edit had set 1.34 — yes line 253 now 1.42.

Now reload and check framing + then test U / U' with the facelet readout open. Batch: reload then click readout.

Still bottom slightly behind the history strip. The target offset of -0.55 didn't lift it much (looks similar). Time is critical (~2-3 min). Quick fix: increase target.y offset to -1.1 and factor 1.5? Or reduce footer overlap by making the strip/pad smaller. Simplest: set cam.target.y = -1.15 and factor 1.42 (keep). Let's do that and one screenshot check, then final U/U' verification.

Actually I can verify moves via the DOM readout without a screenshot: click the "FACELET READOUT" details (84,762), then click U (381,641), inspect DOM text, click U', inspect. The inspect DOM text includes the facelet string. Do these in parallel batches to save time.

Let me do the target edit + reload + open details in one go? Reload must precede clicks. Batch 1: edit (bash node). Batch 2: reload + click details? Reload then click are dependent sequentially but the tool calls in one block run in order presumably. Risky. I'll do: bash edit → browser reload → then one block with click details, click U, inspect, click U', inspect (sequential within block).

Now I'm handling the reload and running through the verification sequence.

Cube fully visible above the panel now. 

Final verification: open facelet readout, click U, inspect, click U', inspect. Buttons: U at (381,641), U' at (437,641), readout summary at (84,762).

Solved facelets: WWWWWWWWWYYYYYYYYYGGGGGGGGGBBBBBBBBBRRRRRRRRROOOOOOOOO ✓ (no '?' — sticker lookup works in the real app).

Now click U (381,641) then inspect, then click U' (437,641) then inspect. Do sequentially in one block? The calls in one block run in order; but I need the animation to finish (~260ms) before inspect. Each tool call has overhead so likely fine. Let's do click U then inspect in one block.

U applied: facelets "WWWWWWWWWYYYYYYYYYRRRGGGGGGOOOBBBBBBBBBRRRRRRGGGOOOOOO" — exactly matching my verified Node model of U ✓ (F top row = RRR, R top = BBB, B top = OOO, L top = GGG). The screenshot caught mid-animation (top layer rotated, buttons disabled).

Now click U' (437,641) and inspect → expect solved string back.

The U' completed: facelets back to the exact starting arrangement `WWWWWWWWWYYYYYYYYYGGGGGGGGGBBBBBBBBBRRRRRRRRROOOOOOOOO`, solved = true, history "U U′", turns = 2. ✓ (Screenshot was mid-animation of U′.)

Now quick check: orbit drag on background + Reset. Do a drag from empty area (e.g., 100,400) to (400,300), then a screenshot, then click Reset (791,689) and inspect.

Time is nearly out. Let me do the drag + screenshot in one call each... I'll batch drag then inspect (with screenshot on inspect? inspect returns images too). Let's do drag, then click Reset, then inspect — but I want to see the orbit change. Do drag → inspect (image shows orbit) → click Reset → inspect. That's 4 calls; probably too many. Combine: drag + inspect in one block (sequential), then reset + inspect in another block.

Background drag orbited the camera (now looking at the L face, orange) without turning any face — state stayed solved ✓. Orbit works.

Now click Reset (791,689) and confirm initial framing + solved.

Reset restored the solved cube and the exact initial framing/camera angle ✓, counters cleared ✓.

Time is up. Final file is saved at /tmp/job-wmyoH3/index.html. Report concisely, noting what's verified and what isn't (Scramble button, drag-on-face turning, wheel zoom, touch pinch, keyboard not exercised in browser — though scramble logic and move engine were verified in Node).