Rubik's Cube · minimax-m3.1-flash

Let's check the three.min.js version and available APIs (e.g., THREE.PlaneGeometry, MeshStandardMaterial, etc.).

Let me write the app. Design:

- Cube: 27 cubies (3x3x3), each a BoxGeometry with per-face materials? Better: use a rounded box? Simpler: build cubies as BoxGeometry with 6 materials — but then each face of the cubie gets a color; for interior cubies all faces neutral (black). Sticker state per cubie per face stored in array, and materials updated.

Approach: Each cubie is a group? Use BoxGeometry with material array of 6 materials indexed [px, nx, py, ny, pz, nz]. For each cubie, we keep state of colors for each of 6 faces (null = black). But when the cube rotates, the cubie's orientation rotates so face directions change. So easier: represent each cubie's sticker colors in cubie-local coordinates, and rotate the cubie group; the stickers move with the cubie automatically since they're attached. But when a layer rotates 90°, the stickers of neighboring cubies that are on the turned layer must transfer? No — with cubie-attached stickers, a layer turn physically moves the cubies; stickers belong to cubies, so they move along. That's correct physics! A sticker is attached to a cubie's face. So each cubie has 6 local face colors, and rotating the layer rotates the cubies physically. Perfect — no state transfer needed.

So: build cubies each as a mesh with BoxGeometry(0.96,0.96,0.96) and 6 materials (or one shared material for the body plus separate sticker planes). Using material array on the box: each material is a MeshStandardMaterial with color; 6 materials per cubie = 162 materials, fine. But stickers need to look distinct: make the box body black and add thin plane stickers slightly offset. That's more meshes (54 visible stickers max... actually each cubie up to 3 outer faces). Simpler: use box with material array where outer faces get color and interior faces black. But then cubie boundaries: gap between cubies of 0.04 gives visible lines against black background... Face color faces will be separated by gaps showing black core -> good visible boundaries.

Better approach for looks: box geometry with slightly beveled? Keep simple: use a BoxGeometry with per-face materials and scale 0.94, and add a black inner core cube of size 2.98 so gaps look black. Actually gaps show background; make background dark gray so it looks fine. Or add a core cube (single dark mesh 2.86) that fills gaps -> nice classic look.

Sticker vs face: The whole face of the cubie is colored — classic cubes have stickers slightly inset but visually ok. To make it nicer, use two meshes: black box cubie (0.98) + 9 sticker planes per face. Hmm, more work but nicer. I'll do: cubie body box with black material (shared), plus sticker planes of size 0.86 at offset 0.5*size+0.005 for outer faces. Sticker plane count: for 3x3x3: 6 faces × 9 = 54 stickers. Each sticker is its own mesh parented to the cubie group. Then state = sticker colors, and rotation handled by moving cubie groups.

Wait but stickers attached to cubie, and cubie group rotation carries them. Yes.

Sticker geometry: PlaneGeometry, rotated per face normal.

Move animation: for a layer turn, group the cubies of that layer into a temporary pivot group, rotate pivot by 90°, then on completion reparent cubies back to root and apply the rotation to cubie's quaternion (so state is exact), i.e. cubie.quaternion.premultiply(rotationQuat) and position updated. Approach: keep all cubies as children of a pivot group per move:

Implementation:
- root = THREE.Group containing all 27 cubies at fixed positions.
- To animate turn of axis/angle: create pivot = new THREE.Group(); root.add(pivot); move cubies whose layer matches into pivot (pivot.attach(cubie) preserves world transform); animate pivot.rotation[axis] from 0 to ±90°; at end, for each cubie in pivot: compute world pos/quat, then root.attach(cubie) (preserves world transform), pivot removed. Since root is identity-transform-ish (no rotation), cubie positions end up snapped correctly. Using attach preserves world transform, so cubie's local position in root = world position (root at origin, no rotation/scale) — good, floats may have tiny errors; round them.

Actually attach computes local matrix from world; since root identity, local = world transform, which after rotation is exactly the snapped grid values (rotation by exact 90° but we should use exact quaternion at end, not interpolated Euler). Use quaternion slerp with exact end value; set final quaternion exactly then update matrix.

Layer selection by axis and sign. Define face mapping:
- U = +Y, D = -Y, R = +X, L = -X, F = +Z, B = -Z.
Cubies with coordinate on that axis = +1 (or -1) belong to layer.

Turn direction (clockwise when viewed from outside): For +axis face (U,R,F), clockwise = -90° about that axis (right-hand rule positive rotation about +Y is counterclockwise seen from +Y looking down... let's check: rotation about +Y by +90° (right-hand rule, thumb +Y): looking from +Y down to origin, positive angle appears counterclockwise when viewed from +Y? Right-hand rule: thumb pointing +Y toward viewer, fingers curl counterclockwise as seen from +Y side. So +90 about +Y = CCW seen from above. Clockwise seen from above = -90 about +Y. So for positive-axis faces, clockwise = -90° about axis. For negative-axis faces (D, L, B), clockwise as seen from outside (from -Y looking up) = +90 about axis? By symmetry: viewing from -Y side, a rotation about -Y axis by +90 is CCW seen from -Y; clockwise seen from -Y = -90 about -Y = +90 about +Y. So negative-axis faces: clockwise = +90 about +axis.

So: dir = +1 for axis positive face? Let's define: clockwise angle about the positive axis: for face on +axis → -90; for face on -axis → +90. Equivalently clockwise about the face's own outward normal = -90 about that normal.

Inverse = opposite.

UI: buttons U, U', D, D', L, L', R, R', F, F', B, B', plus Scramble, Reset. Also maybe a move counter and status.

Camera orbit: drag on background orbits camera. Implementation: pointerdown on renderer canvas, if not on cube? The requirement says dragging background orbits camera without turning a face. Since I don't implement face dragging, all dragging can orbit. But I could also implement drag-on-cubie-face to turn faces — optional; risky. Requirement: "Dragging the background orbits the camera without turning a face." I'll implement face dragging too? No — keep simple but maybe implement face drag turning as bonus? Verification might drag background. If face drag also turns, dragging starting on cube would turn a face — the check says background drag orbits. Simpler: only orbit on drag anywhere. But "without turning a face" suggests maybe they expect face drag to turn? No, "Provide visible buttons" is the required control. I'll implement orbit on drag anywhere (over the cube too) — but hmm, then "without turning a face" trivially satisfied. Fine.

Actually to be safe: implement drag anywhere orbits camera (no face turning at all). That satisfies "drag background orbits without turning a face".

Wheel zoom bounded (e.g., distance 4..14).

Reset: restore solved state (rebuild cubies or reset positions/quaternions and sticker colors) and camera initial position.

State: cubies array with home positions. Reset: for each cubie set position to home, quaternion identity, sticker colors restored to solved (each sticker has its solved color permanently? Sticker color is fixed to the cubie — solved state means sticker color matches its position's face). Since stickers never change color, solved appearance is achieved just by resetting positions/rotations. Correct! Colors are physical stickers, fixed. So Reset = restore cubie transforms.

So store for each cubie: home position, and list of sticker meshes with their fixed color.

Cube orientation also matters: Reset restores camera.

Let me also add keyboard support maybe. Keep it.

Animation: use requestAnimationFrame loop with a move queue. Disable buttons during animation? Requirement: "queue or disable further moves until it completes". I'll queue moves (queue array) and process sequentially. Buttons remain enabled (queueing). Add "busy" indicator.

Also verification of turn + inverse returning stickers to start — I'll implement with exact quaternion.

Let me write code.

Details for stickers: For each cubie at grid pos (x,y,z) in -1..1. For face +X: if x==1 add sticker at position (0.5*s + eps) with rotation looking outward +X.

Sticker plane: PlaneGeometry(w,h) default faces +Z. To face +X: rotateY(+90°). To face -X: rotateY(-90°). +Y: rotateX(-90°). -Y: rotateX(+90°). +Z: no rotation. -Z: rotateY(180°).

Position offset = 0.5*size + 0.012 along normal.

Cubie size 1, spacing 1, so cube total 3. Sticker size 0.86.

Material: MeshStandardMaterial with roughness 0.35, metalness 0.0, and slight emissive? Add lighting: hemisphere + directional + ambient.

Colors: U white, D yellow, F green, B blue, R red, L orange.

Cube root rotated? Keep cube axis-aligned; camera at (5,4,6).

Rounded look: add a subtle "sticker border" by making sticker slightly smaller than face (0.86 vs 1.0) and body black → visible cubie boundaries. Good.

Rotation of sticker relative to face within the plane: stickers should rotate with the cubie face orientation but for solved look orientation doesn't matter. However, during rotation, the sticker square rotates with the cubie — fine.

Ground: a plane? optional, add a subtle grid/plane shadow-less. Maybe skip to keep background drag easy. Add a faint circular "table" plane could intercept raycast; use raycast only on background? Since drag anywhere orbits, no raycast needed.

Let me implement custom orbit controls:
- spherical coords around target (0,0,0).
- pointerdown: record x,y, dragging=true; pointermove: theta -= dx*0.005, phi -= dy*0.005 clamp phi.
- wheel: radius *= (1+delta*0.001) clamp [5, 14]. initial radius ~8.2.

Note the viewport is 1200x800 in the browser tool.

Reset camera: theta = initialTheta, phi, radius.

Also need "keep the cube fully visible initially" — radius 8.5 with fov 45 → cube of size 3 diagonal 5.2; visible height at distance 8.5 with fov45 = 2*8.5*tan(22.5)=7.05 → fits. Good.

Render loop: renderer.setAnimationLoop.

Now the move function.

function queueMove(move) where move = {face:'U', inv:false}.

Process:
axis: U→'y', D→'y', R→'x', L→'x', F→'z', B→'z'.
sign of layer: U,R,F = +1; D,L,B = -1.
layer test: coord along axis == sign (cubie position axis component equals sign).
angle (clockwise seen from outside): rotate about the positive axis by -90*sign? Let's derive: for sign=+1 face: -90 about +axis. For sign=-1: +90 about +axis. So angle = -90 * sign about positive axis. In radians: theta = -sign*Math.PI/2.

Animation: pivot group added to root. For each cubie in layer: pivot.attach(cubie) — but attach requires updateMatrixWorld of the scene. Alternative simpler: compute manually since root has identity transform:
pivot.rotation[axis] = t; but cubies positions need to rotate about origin by the layer rotation — but pivot attached at origin with children repositioned? If I set pivot.rotation and put cubies in pivot at their root-local positions, the pivot rotation rotates them about pivot origin (0,0,0) — which is the cube center. Layer cubies at distance 1 from axis... e.g., layer y=1: cubies at y=1, positions x,z vary; rotation about Y axis through origin keeps y=1. Correct! Rotation about the axis through cube center is exactly the layer rotation.

So: pivot = new Group(); root.add(pivot); for each layer cubie: pivot.add(cubie) but need to preserve position relative to pivot = same as root since pivot at origin identity → just reparent keeping local position (same coords). Since root is at origin identity, positions stay same in pivot local space.

Then animate pivot.rotation[axis] from 0 to theta. At end: for each cubie: apply rotation to its own quaternion and position: cubie.quaternion.premultiply(q) where q = quaternion of rotation about axis by theta (in world = pivot's rotation); cubie.position.applyQuaternion(q). Then reparent to root.

Careful with premultiply: world rotation = parentRot * childRot. Final desired child rotation in root = q * oldRot. Quaternion multiply: q.multiply(oldRot) → premultiply(q) does exactly that. Yes.

Position: p' = q * p. Use position.applyQuaternion(q).

Then set pivot.rotation to 0 and remove pivot (children now empty).

Note: sticker meshes are children of cubie → follow.

Then quantization: positions should be exact integers; applyQuaternion of exact 90° quat gives exact results (with float error ~1e-16). Round to nearest 1e-6? Round to nearest integer to avoid drift: pos.round(). Fine since grid integers.

Also store logical state for scramble? Not needed since scramble = random moves applied through same animation.

Scramble: 20 random moves, queued sequentially, maybe speed. Also reset before scramble? Scramble typically applies to current state. I'll scramble from current state (or reset first — I'll just apply random moves to current state).

Let me also implement a "state string" for display? Not required. But a solver not required.

Add HUD showing last move and move count.

Let's write the file.

Also handle pointer events on canvas; ensure buttons don't trigger camera drag (they're outside canvas).

Also add keyboard shortcuts maybe: u/d/l/r/f/b and shift for inverse. Nice.

Let me write it.

Edge case: buttons should be visible. Use a panel with grid of buttons.

Write index.html now.

For the browser tool, it serves the cwd? It said "agent produced no index.html" — presumably it serves the current dir. Let's write and reload.

Renderer: THREE.WebGLRenderer({antialias:true}); check availability in headless (should work with swiftshader). Add fallback if WebGL unavailable? The check might fail. Let's test.

Write code carefully.

Sticker rotation: I want stickers to also have their own orientation consistent (not rotated 45° etc.) fine.

Let me produce code.

Also "visible cubie boundaries": black body cube of size 1.0 at each cubie, stickers 0.86 — the gap between cubies (1.0 spacing) gives visible dark lines.

Colors:
U white #f5f5f5, D yellow #f2c313, F green #16a34a, B blue #2563eb, R red #dc2626, L orange #f97316.

Hmm, standard: U white, D yellow, F green, B blue, R red, L orange. Good.

Now writing.

For the camera initial position: theta measured: x = r sin(phi) sin(theta)? Let's use spherical: x = r*sin(phi)*sin(theta), y = r*cos(phi), z = r*sin(phi)*cos(theta). Initial theta=0.7, phi=1.05 (from Y axis), r=8.5. y = 8.5*cos(1.05)=4.2, horizontal 8.5*sin(1.05)=7.4 → x=8.5*0.867*0.644=4.75, z=7.4*0.765=5.66. Good view.

Clamp phi to [0.25, 2.9].

Render order: also need the cube centered at origin.

Now write.

Minified. Let's check for "OrbitControls" existence (we don't use it). Check capsule? Not needed. Check MeshStandardMaterial exists: yes likely (r150+). Check whether `THREE.SRGBColorSpace`/`outputEncoding` exists. Let's grep for "sRGBEncoding" and "outputEncoding".

Good, likely r150-ish. I'll use `renderer.outputEncoding = THREE.sRGBEncoding` if available (guarded), and use color space handling carefully. Simpler: use MeshStandardMaterial and set `renderer.outputEncoding = THREE.sRGBEncoding` guarded by check. Colors given in sRGB hex will be converted... In r152+, outputEncoding sRGBEncoding applies gamma. Fine.

Actually to avoid double-conversion issues, keep it simple: use THREE.MeshLambertMaterial or MeshStandardMaterial with lighting, set outputEncoding to sRGBEncoding (guarded). Let's just do it.

Now write index.html.

Cube renders solved. But the cube appears very large — camera radius 8.6 but cube fills most of screen and bottom cut? Actually it fits. Hmm it looks bigger than expected: cube appears ~500px tall of 800. Fine but "fully visible" — yes visible. Maybe increase radius slightly to 9.5 for comfort. Also the visible faces: U white, F green, R red — but the green face appears on the left which is F? Camera at theta 0.72 → x positive, z positive → sees +X (R red) and +Z (F green). Screenshot shows green left, red right — consistent.

Now test a turn and its inverse. Click R, wait, click R'. Verify state returns.

Note the cube looks like it fills a lot; let's zoom out a bit (radius 9.6) to ensure full visibility.

Let me test interactions via browser clicks. First test state function via inspect? The browser tool only supports click/drag/key/inspect. Inspect gives DOM and console. I can use console logs? The inspect returns console messages. I could add a console.log for verification. Alternatively use `browser action=inspect` after triggering something that logs state.

Better: temporarily add console.log output in reset/move for testing? I can add a permanent debug hook: window.__cube.state(). To read via browser inspect, maybe console output only shows logs. Let's just log state changes to console with console.log in performMove completion (maybe too noisy). I'll add a log of state hash after each move — could be fine but noisy. Instead, let's use the DOM: update status text to include a state signature? Could show "Solved" status — that's the check. isSolved() compares positions+quaternions to home; that's a strong check for turn+inverse returning stickers.

But note: turn+inverse returns cubies to home positions only if the same cubies return — yes each cubie returns to its home position with identity rotation. Actually a cubie in the turned layer returns to home position and identity rotation after U then U'. Yes.

However "checking that the visible stickers return to their starting arrangement" — cubie position+rotation identity ⇒ sticker arrangement identical. Good, but colors are fixed to cubies so if positions restore, colors restore.

Also I should verify the move direction semantics (clockwise). Let's check: U turn clockwise viewed from top should move the front-top row to the left? Standard: U moves the front row stickers to the left face... Let's verify visually: after U, top layer's front stickers move to the left side (i.e., F→L). My implementation: angle = -sign*90° about +Y for U (sign=+1) → -90° about +Y. Rotation by -90° about Y: point (x,z) → ? Rotation about Y by angle θ: x' = x cosθ + z sinθ, z' = -x sinθ + z cosθ. For θ=-90: x' = -z, z' = x. A sticker on F face (+Z, position (0,1,1)) → x'=-1, z'=0 → moves to L face (-X). So F→L. Standard U clockwise (viewed from above, i.e. from +Y): front row goes to the left. Yes U clockwise moves F→L. Correct.

Wait, careful: viewed from above, clockwise means going F→R? Let's think: looking down from +Y at the cube, with +Z pointing toward viewer (front, down in the top-view picture?) Standard top view: U face seen from above with F at the bottom of the view, R at right. Clockwise rotation: bottom edge (F) moves to left edge (L). Yes clockwise: bottom→left. So F→L correct. ✓.

R turn: standard R clockwise (viewed from right, +X) moves F→U. My formula for R: sign=+1, angle=-90 about +X. Rotation about X by θ: y' = y cosθ - z sinθ, z' = y sinθ + z cosθ. θ=-90: y' = z, z' = -y. Sticker at F (0,0,1) with y=0,z=1 → y'=1, z'=0 → U. So F→U ✓ (standard R clockwise moves front column up to top).

F turn: sign +1, angle=-90 about +Z: rotation about Z by θ: x' = x cosθ - y sinθ, y' = x sinθ + y cosθ. θ=-90: x'=y, y'=-x. Sticker at R face (1,0,0) → x'=0,y'=-1 → D. So R→D for F clockwise ✓ (F clockwise moves right column down to bottom... standard F clockwise: U→R→D→L. U sticker at (0,1,0) → x'=1,y'=0 → R ✓).

D: sign=-1, angle = +90 about +Y: (0,0,1)→x'=1? x'=x cos + z sin = z =1, z' = -x sin + z cos = 0 → R. D clockwise viewed from below moves F→R? Viewed from bottom (-Y), clockwise: in bottom view with F at top of the picture... standard: D moves the bottom layer like F→R? Let's check standard cube: D (clockwise viewed from bottom, i.e., looking at D face) cycles F→L? Hmm.

Convention: D turn clockwise when viewed from the bottom (looking up at D face from below). Looking from below with F face at the top of your view... Take bottom view: you look up along +Y; orient so F (+Z) appears at top. Then clockwise rotation in that view maps top→right, i.e., F→R? In the bottom view, if +Z (F) is up and looking from -Y toward +Y, then +X (R) appears on the left (because viewing from opposite side flips handedness). Hmm.

Easier: use consistency: D should be the inverse direction of U's motion in a sense? No, D is a separate layer but the same rotation direction applied to bottom layer: standard D move is clockwise viewed from the D face (below). Cube notation: all moves are clockwise when viewed directly at the face being turned. For D, viewed from below. Viewed from below, the F face's bottom row goes to... A clockwise rotation about the face normal (-Y) by -90° about -Y = +90° about +Y. And +90 about +Y maps F→R per computation (x'=z=1). Now is that consistent? Viewed from below along +Y direction, with the standard "look at the face" orientation: face D's outward normal is -Y toward viewer. Clockwise = -90° about the outward normal (-Y) = +90° about +Y. ✓ That's exactly what I implemented (clockwise about outward normal). And for U: clockwise = -90° about +Y = implemented as -90 about +Y ✓. And for R: clockwise = -90 about +X ✓. So all faces: rotate by -90° about the face's outward normal. My formula angle = (inv?1:-1)*sign*90 about positive axis: for sign=+1 (positive face), -90 about +axis = -90 about outward normal ✓. For sign=-1, angle = +90 about positive axis = -90 about outward normal (which is -axis) ✓. Consistent.

Now, verify with a real cube: R clockwise viewed from right side (+X outward toward viewer). Rotation -90 about +X maps F→U ✓ matches known R behavior (R brings front column to top). Yes, standard R: the right column goes up... R moves U→B→D→F→U? Actually standard R turn: the F right column moves to U? Hmm, R moves the right column upward: front-right column goes to top-right. Yes R: F→U, U→B, B→D, D→F. ✓.

Good.

Now let's test in browser: click R, then R', and check status shows Solved, and also visually. But status is only updated after animation completes. Let's click R then wait then click R'.

Also there's an issue in resetAll: it removes pivot groups by checking child.type === 'Group' — cubie meshes are Groups too and children of cubeRoot! So the loop `cubeRoot.children.slice().forEach` would re-parent every cubie (which is fine — attach preserves transform) and then remove them from cubeRoot! That's a bug: it would remove all cubies from the scene.

Wait cubeRoot.children are the 27 cubie groups (type 'Group'). The condition removes all of them. Bug! But I set positions before that... The result: cube disappears. Need to fix: track pivots explicitly with a variable `activePivot`.

Let me restructure: keep a variable activePivot; resetAll only handles that. Also cubies list holds references so re-adding is fine, but simpler: use activePivot.

Also the stickers recording loop: `c.mesh.children.forEach` skipping first child — body is first child, stickers after. Fine but unused.

Also potential issue: cubie mesh type 'Group' and cubeRoot children. Fix reset.

Another: during reset while a move is animating, the animating flag remains true and its rAF loop continues, re-parenting. Better: cancel animation on reset. Use a token/generation counter: increment resetGen; in step, if gen changed, abort.

Let me implement: var gen = 0; performMove captures g = gen; in step, if (g !== gen) { done-skipped; return; }. And reset increments gen, sets animating=false, queue cleared, restores cubies.

Careful: pump() sets animating true; the done callback sets animating false. If aborted, we must set animating=false and not call done (to avoid double-processing). Let's handle.

Let me apply the fix.

Also adjust camera radius to 9.4 for full visibility and slight position.

Also the sticker colors: green appears mint-ish (0x18a558 with sRGB encoding, lighting bright). Fine.

Also the cube's bottom appears cut off? Bottom vertex at ~690px, screen 800 — fine.

Let me fix and re-test.

Wait: resetAll restores cubies positions/quaternions but the in-flight pivot children were reparented via attach, which preserves world transform — then we set positions to home anyway. Good.

Also: `cubeRoot.attach(cm)` in reset: the pivot had rotated; attach preserves world transform, so cubies get their rotated world pos, then we override with home. But we also need to reset quaternion — we do set identity for all. Good.

However, order: the reset loop sets positions/quaternions BEFORE the abort code runs (abort happens after). The attach() would then override positions with pivot-rotated positions. So I must abort first, then set positions. Let me reorder.

Now test in the browser: reload, click R, wait, click R', check status shows Solved. The browser click action clicks at coordinates. Button positions from earlier screenshot: R button at (67, 677). Let's click R, then take motion/screenshot, then click R' at (67, 725)... but R' button is at row with R at x=67? Grid is 3 columns: col1 x≈67, col2 x≈122, col3 x≈181. Rows: row1 (U,U',D) y≈560, row2 (D',L,L') y≈625, row3 (R,R',F) y≈680, row4 (F',B,B') y≈735.

Wait earlier screenshot rows: U,U',D at y=560; D',L,L' y=625; R,R',F y=680; F',B,B' y=735. But layout may have changed slightly since radius change doesn't affect panel. Actually earlier screenshot shows R at (67,677) row 3 and R' at (122,680).

Let me reload and click R, wait ~0.5s, screenshot, then click R', screenshot.

Also I should verify the sticker state programmatically. The browser tool's inspect returns console messages; I can add a temporary console.log? Instead, the status text "Solved" is a good check (isSolved compares positions and quaternions).

But isSolved checks positions and identity quaternion, which fully determines sticker arrangement given fixed sticker colors. Good enough.

Let's do the test.

Cube fully visible. Now click R (at 67, 677) and screenshot mid-animation / after.

Mid-animation of R: the right layer is rotating (shown tilted). Good. Now wait and screenshot to see finished state, then click R'.

The click action returned immediately. Let me take a screenshot after some time.

R turn completed correctly: U face right column shows yellow (D came up to U? R moves D→F... wait). R clockwise: F→U, U→B, B→D, D→F. So the right column of U should show... U's right column moves to B, and F's right column (green) moves to U. But screenshot shows U's right column yellow and F's right column blue.

Hmm. Let's check: visible faces are U (white top), F (green left face), R (red right face). The U face's right column is yellow → the D (yellow) stickers came to U. That means D→U. And F's right column is blue → B→F. And R's right face still red (red face rotates in place, its own stickers rotate).

So my R did D→U, B→F. That corresponds to R' (counter-clockwise): R' cycles F→D→B→U→F? Standard R: U→B? Let's recompute. Hmm, I derived earlier F→U for -90° about +X. Let's recompute the rotation formula carefully.

Rotation about X axis by angle θ (right-hand rule, thumb along +X): a point (y,z) rotates: y' = y cosθ - z sinθ, z' = y sinθ + z cosθ.

Check: θ=+90: (y=0,z=1) → y' = -1, z' = 0. So +Z → -Y (F→D). And +Y (U) → y'=0, z'=1 → F. So +90 about +X: U→F, F→D, D→B, B→U.

I earlier wrote θ=-90: (0,1)→ y' = z =1?? let's redo: θ=-90, cos=0, sin=-1: y' = y*0 - z*(-1) = z; z' = y*(-1) + z*0 = -y. So point (y=0,z=1) (F) → y'=1, z'=0 → U. So -90 about +X maps F→U. That's what I said. But the render shows D→U i.e. +90 about +X applied.

So my angle sign must be opposite to intended. Let's check my code: angle = (mv.inverse ? 1 : -1) * sign * (Math.PI/2). For R: sign=+1, not inverse → angle = -90°. Then quaternion setFromAxisAngle(X, -90°) and pivot rotation about +X by -90 → F→U. But observed D→U which is +90.

Hmm, maybe I mislabeled which visible face is F vs R! Camera at theta=0.72: camera.position.x = r*sin(phi)*sin(theta) > 0, z = r*sin(phi)*cos(theta) > 0. So camera is at +X,+Z, looking at origin. It sees the +X face (R, red) on the right? and +Z face (F, green) on the left. In the image, green is on the LEFT, red on the RIGHT. With camera at +X+Z looking toward origin: the +Z face appears on the... The camera's right direction is perpendicular: right = normalize(cross(forward, up)). forward = -(sin θ, ., cos θ) direction = (-sinθ, 0, -cosθ). up=(0,1,0). right = forward × up? Three.js camera looks down -Z of its own frame; screen right = camera's local X. For camera looking along f=(-sinθ,0,-cosθ), with up (0,1,0): local X (right) = normalize(cross(up, -f))?? Let's just: camera at (x>0, z>0). Point on +Z face (F) is at z=1. From camera at (4.7, 4.9, 6.6)-ish looking at origin: the F face (z=+1) is closer to the camera on the z+ side; screen-left or right? Screen right vector r = f × up? Using right-handed: right = normalize(cross(f, up))? cross(f,up) with f=(-0.66,0,-0.75), up=(0,1,0): cross = (f.y*up.z - f.z*up.y, f.z*up.x - f.x*up.z, f.x*up.y - f.y*up.x) = (0*0 - (-0.75)*1, (-0.75)*0 - (-0.66)*0, (-0.66)*1 - 0) = (0.75, 0, -0.66). So screen-right direction in world ≈ (+0.75, 0, -0.66) → pointing toward +X and -Z. The R face center is at +X: dot with right = +0.75 → R appears on the right ✓. F face at +Z: dot = -0.66 → left ✓. Consistent with image: green (F) left, red (R) right. Good.

So the R column: the rightmost column of the visible green face is the R-layer column ✓, and the right column of U is the R-layer column.

Observed after clicking "R": U right column = yellow (D), F right column = blue (B). So D→U and B→F. That's the rotation where +90 about X maps D→U? +90 about X: U→F, F→D, D→B, B→U. That gives B→U and U→F. Not matching.

Rotation -90 about X: F→U, U→B, B→D, D→F. That gives D→F (yellow into F right column) and B→U (blue in U column). But observed: yellow in U column, blue in F column. That's the opposite mapping!

So the applied rotation was +90 about X?? Under +90: U→F: the U column (white) would move to F, and D→B (not visible), B→U: blue to U column, F→D: green to bottom. So U column would be blue, F column white. Observed: U column yellow, F column blue. Neither.

Hmm! So maybe yellow in U column and blue in F column means D→U and B→F. Which rotation does that? Let's list rotations about X: identity, ±90, 180.
- -90: F→U, U→B, B→D, D→F.
- +90: U→F, F→D, D→B, B→U.
- 180: F→B, B→F, U→D, D→U.

Observed D→U and B→F — that's 180°! But it's a quarter turn... unless the animation captured a mid-rotation? No, screenshot after completion shows a clean arrangement.

Wait — maybe I misread the image. Look again: Top face: left 2 columns white, right column yellow. Front-left face (green): left 2 columns green, right column blue. Right face (red): all red.

180 about X would give U right column = D (yellow) ✓ and F right column = B (blue) ✓. So it looks like a 180° rotation of the R layer!

Why? Because of the ease function! e = t<0.5 ? 2t² : -1 + (4-2t)t. At t=1: -1 + (4-2)*1 = 1 ✓. Hmm that's fine, ends at 1.

But wait: pivot.quaternion.slerp from identity to q — fine.

Hmm, maybe the issue: pivot.add(c.mesh) — when adding, THREE's Object3D.add does NOT preserve world transform (it keeps local transform as-is, but here pivot is at identity so same). Actually add() reparents keeping the same local position — since pivot has identity transform and cubeRoot is identity, world positions unchanged ✓.

But then pivot.quaternion.copy(from).slerp(q, e) — rotating the pivot rotates children about pivot origin ✓.

Then at the end we premultiply q into each cubie quaternion and applyQuaternion(q) to positions — and cubeRoot.attach(c.mesh) preserves world transform. Wait: cubeRoot.attach(mesh) sets mesh's parent to cubeRoot and computes local transform from world matrix. But we've already applied q to the cubie's local quaternion/position (which were relative to the pivot). Now cubeRoot.attach computes world = pivotWorld * cubieLocal = q * (q*oldRot) → double rotation! Because the cubie's local transform was already updated to include q, and attach composes with the pivot's rotation q again.

Yes! That's the bug: double rotation → net 180° for a 90° turn. Matches observation.

Fix: don't premultiply/applyQuaternion before attach. Instead: either (a) use attach (which composes pivot rotation automatically) and skip manual baking; or (b) remove pivot without attach but manually bake.

Option (a) is cleanest: after setting pivot.quaternion = q, call cubeRoot.attach(c.mesh) for each — the world transform is preserved, so the cubie ends up rotated by q around the pivot origin, in cubeRoot local coords = world coords (cubeRoot identity). Then remove pivot. And the cubie's local quaternion automatically becomes q*oldRot ✓ and position q*p ✓.

But careful: attach uses matrixWorld, which requires updateMatrixWorld. Object3D.attach calls this.updateWorldMatrix? Let me check three.js source for attach:

attach(object) { this.updateWorldMatrix(true, false); _m1.copy(this.matrixWorld).invert(); if (object.parent !== null) { object.parent.updateWorldMatrix(true, false); _m1.multiply(object.parent.matrixWorld); } object.applyMatrix4(_m1); object.removeFromParent(); object.matrixWorldNeedsUpdate = true; ... }

Yes, attach handles it properly (three r1xx). And it uses updateWorldMatrix(true,false) so children's world matrices get updated. Good.

So fix: remove the manual premultiply/applyQuaternion and rely on attach. But floating point: pivot.quaternion.copy(q) exactly → matrix exact-ish, fine. Positions may have tiny float error; round to integers after attach.

Also I should double check the three.min.js version's attach implementation exists similarly (r150+). Let's grep minified for "attach" function body.

Alternatively safest: do the baking manually and then reparent without preserving world transform: pivot.remove(child) then cubeRoot.add(child) — since pivot is at origin identity-ish? No, pivot has rotation q; removing a child from pivot and adding to cubeRoot keeps the child's local transform (relative to pivot) → that loses the pivot rotation. But if I bake q manually into local transform before removing, then adding to cubeRoot gives the right result: local = q*old. Yes! Because I manually applied q to quaternion and position, and pivot's own transform is ignored when reparenting via add (local transform kept).

Wait but add() keeps local transform as-is: mesh.local = q*old ✓ and position = q*p ✓. That's exactly right and independent of attach semantics. So: bake q manually, then pivot.remove(mesh); cubeRoot.add(mesh). That avoids attach entirely. But careful: pivot.remove then cubeRoot.add — order fine.

However there's subtlety: after baking, the mesh's world matrix when in pivot = pivotWorld(q) * (q*old) = q*q*old — but we immediately reparent, so no issue.

So fix: replace the final block to bake then pivot.remove + cubeRoot.add (not attach). Let me do that and also round positions.

Let me also double check the layer filter uses Math.round(p.x) — positions are integers ✓.

Additionally, after the fix, verify direction: R should give F→U (green to U column).

Let me apply the fix.

Note: during animation, cubies are children of pivot which is child of cubeRoot — cubeRoot.add(cubie) at the end reparents correctly.

Also the reset while animating: pivot children moved to cubeRoot via add — but their local transform includes pivot rotation? No: pivot.remove(cm) then cubeRoot.add(cm) keeps cm's local transform (which is in pivot-local space, i.e. pre-rotation since the rotation lives in pivot.quaternion). Then reset sets positions to home and quaternion identity. Fine.

Now reload and test R then R'.

Solved state looks good. Now click R and check the result.

Now R turn: U right column is green (F→U ✓), F right column is yellow (D→F ✓). Correct standard R turn.

But status still shows "Turning… (1 queued)" and log "R" — the status hasn't updated after completion? The log shows "R" meaning moveCount incremented, log updated. But the text says "Turning…". The statusText updates in done() → updateStatus() sets busy = animating || queue.length>0; at that moment animating is still true? In performMove's done callback we call updateStatus() BEFORE setting animating=false? Let's look:

```
performMove(mv, function () {
  moveCount++; lastMoves.push(mv); ...
  updateStatus();
  animating = false;
  pump();
});
```
Yes — updateStatus() called while animating is still true → shows busy. Fix: set animating=false before updateStatus.

Also the status dot yellow. Fix ordering.

Also note the cube's bottom-right yellow column: fine.

Let's fix and also verify R' returns to solved.

Wait: pump() is called after updateStatus; but when queue has more items, pump starts the next move which sets animating=true, but status won't update to "Turning" until the next completion. Minor: updateStatus after pump. Let me restructure: in pump(), when starting a move, call updateStatus() to show busy.

Modify pump:
```
function pump() {
  if (animating || queue.length === 0) return;
  animating = true;
  var mv = queue.shift();
  updateStatus();   // show busy immediately
  ...
}
```
And in done: animating=false; ...; updateStatus(); pump(); → pump sets animating true and updateStatus shows busy. Order fine.

Let me add updateStatus() in pump after setting animating.

The screenshot captured mid-animation (R layer rotating). Status now says "1 move applied" — hmm, it says 1 move applied while the animation appears in progress? This screenshot may be from the moment the animation finished... but the cube shows mid-rotation. Actually the screenshot might be taken slightly before the final frame render. Anyway.

Now click R' (at x=122, y=677) and then check status becomes "Solved" and visual solved.

R then R′ returns to solved appearance, status "Solved", log "R R'". 

Note: stickers of R face rotated (individual R stickers turned) — with cubie-attached stickers, the R face's own stickers rotate in place (rotation of the sticker square about its normal) which is invisible for square stickers. Fine.

Now test orbit drag on background, then Reset.

Drag from a background point, e.g. (900, 600) → (1000, 500).

Orbit worked — camera moved to view the green F face from the right and below (now we see green front, yellow bottom, orange left). No face turn happened (still "Solved", log R R'). ✓

Hmm, the phi decreased by dy*0.006 = (460-600)*0.006 = -0.84 → phi increased → camera lower. Dragging up moved camera down (inverted look). Typical orbit: dragging up rotates the object up = camera goes down... In OrbitControls, dragging up moves camera up? In OrbitControls, dragging the mouse up rotates the camera upward over the top (i.e., camera elevation increases) — actually dragging up pulls the top of the object toward you, meaning the camera moves up. Standard: dragging down moves camera up. Hmm, in OrbitControls: rotateUp(2π * dy / height) where dy = current - previous; drag down (dy>0) → rotateUp positive → phi decreases → camera moves up. So dragging down raises the camera. Mine: dragging down (dy>0) → phi -= dy*0.006 → phi decreases → camera rises. Same as OrbitControls ✓.

Now test Reset after orbiting.

Reset restored the initial camera framing and solved appearance ✓.

Now test Scramble: click Scramble and confirm the cube gets scrambled, moves queue properly. Then Reset again.

Also test wheel zoom bounds.

Let's click Scramble.

Scramble is animating with the queue (21 queued). Wait a few seconds and check the final scrambled state.

Also note the mid-animation rendering shows layer rotating correctly.

Let's wait by taking screenshots until status shows "22 moves applied".

Scrambling works — mixed colors, queued moves still running. Wait for completion then test Reset.

Note: the cubie boundaries look great.

Let me wait, then click Reset, then check status shows Solved and camera restored.

Also test wheel zoom bounds. Let me do scroll test: browser scroll action with delta. Use action=scroll with delta -500 at some coordinate, check cube grows but stays bounded, then scroll +1500 to zoom out and check it doesn't go too far.

First wait for scramble to finish.

Scramble completed with a properly scrambled cube (22 moves applied). Now test Reset and wheel zoom.

Let me test scroll zoom bounds first: scroll down (zoom in) a lot at (600,400), then reset. Actually Reset restores camera. Test wheel zoom: scroll with delta -600 (zoom in).

The scroll action didn't change the camera — the cube looks identical. Possibly the browser tool's scroll dispatches a wheel event on the element under the cursor; my listener is on the canvas element with passive:false and preventDefault. Hmm, it looks unchanged (radius unchanged). Maybe the scroll went to the page (body overflow hidden). Or the tool's scroll uses mouseWheel events which should hit the canvas.

Possibly the tool scrolls with `scroll` action on the document, generating wheel events on the target element at coordinates. The canvas covers the whole area. Should work.

Maybe it did work but delta -600 → zoom in should make cube bigger. Cube size looks identical to before. Let me test by dispatching a wheel event directly? I can't run JS through the browser tool (no eval action). Hmm.

Let me check if scroll works at all — maybe the tool's scroll event has deltaY sign and my handler clamps with Math.sign(deltaY)*min(|deltaY|,100)*0.0015 = -0.15 factor → radius *= 0.85 → 9.4→8.0. That's a modest zoom; screenshot may show slight change. Comparing cube widths: before ~470px, after ~470px. Hard to tell.

Let me do a bigger scroll test: several scroll actions with delta -1600 (max). Actually delta range max 1600.

Also maybe the tool sends scroll to the page which doesn't bubble to canvas... wheel events do bubble to window but I listen on the canvas element directly; if the event target is the canvas, fine.

Let me try scrolling and take a screenshot to compare. Alternatively add a listener on window instead of canvas for wheel — more robust. Let's change the wheel listener to window (with passive:false) so any wheel anywhere zooms. But the buttons panel is separate; wheel over the canvas is the main case. I'll attach to window to be safe.

Let me also display the radius in the status so I can verify. I'll add radius to the status panel text.

Let's edit: wheel listener on window; status shows "zoom x.x".

Zoom-in works (9.4 → 7.4). Now test zoom-out clamp: scroll +1600 several times to reach 14 max.

Zoom out works (7.4 → 9.0). Each scroll event is one wheel notch apparently; the tool sends one event with deltaY 1600 but clamped to 120 in my handler → step = 0.216 → radius*1.216. Hmm 7.4*1.216=9.0 ✓. But scrolling out should increase radius — deltaY>0 → step=+0.216 → radius*1.216 = 9.0 ✓ yes correct (zoom out).

Wait, but for zoom in, deltaY=-1600 → step=-0.216 → 9.4*0.784=7.4 ✓.

The clamp uses min(|deltaY|,120) so big scrolls are limited per event; fine. But a user scrolling fast might want faster zoom. It's fine.

Bounded: min 5.0 max 14.0 enforced ✓.

Now, test the reset button (restores camera 9.4) — currently at 9.0 zoom. Click Reset and verify "zoom 9.4" and Solved.

Also test the U face turn correctness and D/L/B/F direction. Let me verify U visually: click U and check top face rotates (front row of white goes to left). And F: check.

Let's click Reset first.

Reset restores zoom 9.4, solved ✓.

Now verify a few other face directions visually:
- U: expect F top row → L, so the front face's top row becomes... U moves F's top row to L, and R's top row → F. So the front (green) top row should show red (R stickers come to F? no: U clockwise cycles F→L→B→R→F, so R→F means the front top row shows red). Let's check: earlier computed for U: F→L. And R→F? Rotation -90 about +Y maps (x,z)→(-z,x). Point on R face x=1,z=0 → x'=0, z'=1 → F ✓. So after U, front face top row = red, and left face top row = green.

Let's click U and check.

Also verify L, F, D, B at least once each. Time budget ok.

Let me click U (67, 560).

Screenshot captured mid-animation (top layer rotating). Let me take another screenshot after it settles to confirm U result (front top row red, left top row green).

Wait — the animation appears to have the top layer lifted/rotating oddly: the top face looks shifted up-left. It's mid-animation at maybe 50%, so the layer is rotating about the Y axis and perspective makes it appear shifted. Fine.

Take screenshot again.

After U: front face top row is red (R→F ✓), right face top row is blue (B→R ✓), i.e. cycle F→L, L→B, B→R, R→F ✓ correct U clockwise.

Now check L, F, D, B quickly. Let's do F and check: F clockwise cycles U→R→D→L→U. After F: right column of U should show... U's right column (white) moves to R face, so R face's left column? Hmm R face column nearest F becomes white? Actually F turn moves U front row → R front column. So R face's front column becomes white. And D front row ← L front column (orange).

Let me click F (at 181, 677) after resetting first (to have clean state). Let me reset then F.

Also I want to check the L turn and B and D but those faces aren't visible (L and B are hidden). I can orbit to see them. Time is limited (15 min budget, we've used a fair amount). Let me be efficient: check F now, then reset, then orbit to see B and L and D.

Actually a quicker check of all 6 directions: I can reason mathematically since all faces use the same rule (clockwise about outward normal) and I verified U and R visually, plus F should follow. The rules are uniform, so D/L/B are consistent by construction.

Let me still check F visually, and check L/B by orbiting.

Reset first then F.

Reset works ✓ (solved, initial framing).

Now click F (181, 677) and check: F clockwise cycles U→R→D→L. Expect: R face's front column white (from U), D front row red (from R)? wait R→D: R's front column goes to D's front row → D shows red along front row. L front column ← D? cycle U→R→D→L→U: D→L so L gets yellow front column. U front row ← L front column (orange).

Let's click F and screenshot.

Note: current view shows U, F (green, left), R (red, right). After F: U front row orange, R front column white, D front row red.

Let's do it.

Wait — the log says "R'" but I clicked F at (181,677)? The log shows "R'". Hmm! Let me look: the log element shows "R'" and status "1 move applied". But the cube shows the F face's front column white and U's front-right row blue — that's an R' turn? R' moves U→F? R' cycles F→D→B→U→F: so U→F means white goes to F's right column ✓ (image shows F right column white). And B→U: blue goes to U's right column ✓ (image shows U right column blue). So indeed the applied move was R′, not F!

I clicked at (181, 677) which should be F... but the R' button is at x=122. Hmm, the click reported at 181,677 hit R'? Let's check the screenshot layout: row 3 = R (67), R' (142), F (216)? In the current screenshot: "R clockwise" at x=67, "R' counter" at x=142, "F clockwise" at x=216. Row 4: F' at 67, B at 142, B' at 216.

I mis-assumed column positions earlier. In the screenshot the buttons are: row1: U(67), U'(142), D(216); row2: D'(67), L(142), L'(216); row3: R(67), R'(142), F(216); row4: F'(67), B(142), B'(216).

Earlier I clicked (122, 677) intending R' and it did apply R' — and the status showed Solved after R then R'. Wait, earlier I clicked (67,677)=R ✓ and (122,677)=R' ✓ (close to 142? 122 might still be within R' button if button spans ~105-180). Anyway.

So my click at (181,677) hit F? The log says R'. Button F spans roughly x=190-245. 181 is in R' (ends ~180). So it hit R'. Fine — so F not yet verified.

Let's click F at (216, 677) and check.

Also note this confirms R' behaves correctly: white F column ✓.

Also earlier the "U" click at (67,560) → U button row1 col1 at y=560 ✓ correct.

And earlier L/D/B buttons untested. Let me now: click F at (216,677).

The F layer is rotating (mid-animation). Let me screenshot after it settles to verify F direction: expect U front row orange (L→U), R front column white (U→R), D front row red (R→D).

Wait, F clockwise cycle is U→R→D→L→U. So R's front column should get white from U ✓, D's front row gets red from R, L's front column gets yellow from D, U's front row gets orange from L.

Let's check.

Let's verify the F result against expectations. State before F was after R': U right column blue, F right column white, others solved-ish (R' affects only R layer: U↔F? R' cycles F→D, D→B, B→U, U→F. So after R': F right column ← U (white) ✓, U right column ← B (blue) ✓, D right column ← F (green), B right column ← D (yellow)).

Then F (front layer, z=+1) clockwise: cycle U→R→D→L→U for the front column/sticker rows.

Expected after F:
- U front row: from L front column → orange? But the image shows U front row = yellow (the row adjacent to the front edge shows yellow in the two middle? Let me look: top face front row shows yellow in the middle two cells, and blue in the right two?). Hmm, the top face in the image: back row white; middle row white white blue?; front row: green? Actually the top face shows a yellow cell and blue cells.

This is getting complex; I trust the uniform rule.

Actually wait, there's an issue: the F face (green, left-front) after F should show green in its front layer (the F face stickers rotate within F face, staying green ✓) — indeed the front-left face shows green except bottom row white. Hmm, the front-left face is the F face: it shows green on top two rows of left column and white on bottom row. That bottom-row white shouldn't be affected by F... unless the visible left face is F and the bottom row white came from R' (D right column ← F green...). Hmm.

Hold on. Which face is which in this image? Camera at theta 0.72 → +X and +Z visible: F (green, +Z) on the LEFT, R (red, +X) on the RIGHT. The image shows green face left-front and red face right. But the green face's bottom row is white and its right column... hmm, the visible left face shows: column1 (leftmost): green, green, white; column2: green,green,white; column3: green, white, blue.

Wait, that's the F face showing white in the bottom row and white/blue in the right column. But F face stickers are all green (F face stickers stay on F face; F turn rotates them within the face). So the F face should be entirely green after R' F. But the image shows non-green on the F face!

Unless... the face I think is F is actually L? No, L is orange.

Hmm, actually maybe the visible left face is the F face and my expectation is wrong: the F face's own stickers stay green but stickers from other faces can move INTO the F face? No! A sticker on the F face stays on the F face during an F turn; stickers from U/R/D/L move to R/D/L/U positions but those are adjacent faces, never onto F. So the F face must be all green.

So the image shows the left face with green/white/blue — that suggests I'm misreading which face is which, OR there's a bug.

Wait: maybe the camera has rotated? No, camera unchanged (theta 0.72). Hmm.

Let me re-look at the image: The visible left-front face is green with white squares at bottom-left 2 cells and white/blue in right column. The visible right face is red. The top is white with yellow and blue.

So the F face (green) is partially white/blue → bug? Unless that face is not F but... could it be that the cube's orientation changed? The cubies rotate; the F face position in space is still z=+1, with stickers there being green only if no other stickers moved to the front plane. Sticker colors move with cubies; a sticker on the U face of a cubie at z=+1 stays on that cubie's +Y local direction... but after rotations, a cubie's local +Y might point to +Z in world space! Yes! That's the thing: stickers are attached to cubies and rotate with them, so a sticker that was originally on U can end up facing +Z (front) after the cube is scrambled. That's physically correct — the front face can contain yellow/white stickers from other faces.

But wait, for an F turn, the stickers of the F layer cubies rotate within the F layer: the U-face sticker of a front-top cubie rotates to face R (world +X) ✓, and the F sticker stays facing F ✓. So the F face should still be all green after F... plus before F, R' had put white/blue stickers in the F face's right column (from U and B). Yes! R' moves U→F and B→U: so F's right column got white (from U) and F's... let's see R' cycle: U→F, F→D, D→B, B→U. So F right column ← U right column = white ✓ (image earlier showed F right column white ✓). And U right column ← B = blue ✓ (image showed U right column blue ✓). D right column ← F = green, B right column ← D = yellow.

After F: F layer (z=+1) rotates: U front row → R front column, R front column → D front row, D front row → L front column, L front column → U front row. The F face stickers all stay green. But the image shows the left (F) face with white at bottom row and white/blue right column!

Contradiction → unless the visible left face is NOT F. Hmm, maybe it's the L face? no.

Let me reconsider the camera: theta = 0.72 rad, phi = 1.06. camera.position.x = r sinφ sinθ > 0, z = r sinφ cosθ > 0. So camera is in the +X/+Z octant. The visible faces are +X (R) and +Z (F). Screen-left = -X? We computed screen-right ≈ (0.75, 0, -0.66) so +X is right, +Z is left. So the left face is F (green), the right face is R (red). Image: right face is red ✓, left face is green ✓. So the left face IS F, and it shows white/blue → inconsistent with expectation!

Unless the screenshot shows the cube mid-animation of F? The status says "2 moves applied" so F finished. Hmm, but maybe the render happened right at the end.

Wait — maybe I misread the image. Let me zoom into the image mentally: The left face in the image: it appears to have a large green region in the upper-middle-left, white at the bottom row, and the right portion (adjacent to the vertical edge between F and R) has white and blue cells.

Hmm! Actually maybe what I see is: the F face = the big face on the left with green in the upper-left 2x2 area... Honestly the "white bottom row" might be on the D face? No, D isn't visible from above.

Hmm, is it possible the screenshot shows the cube where the visible left face is actually the U... no.

Let me just take a fresh screenshot and analyze the pixel layout more carefully by cropping? I can't crop with tools easily. But I can use the browser "inspect" DOM - no image analysis.

Alternative: verify programmatically. I can add a temporary debug function that prints the state to console and check via inspect console output. That's more reliable. Let me add a console log of the full sticker arrangement after each move (temporarily), then use the inspect action to read console messages.

Let's implement a debug function: for each of the 6 world directions, list the colors of the 9 stickers facing that direction. Print as JSON. Then I can check that after F the front face (+Z) is all green.

I'll add window.__cube.faceColors() and a console.log on each move completion (temporarily). Then trigger moves and read console.

Let's do it: add function:

function faceColors() {
  var out = {};
  ['U','D','F','B','R','L'].forEach(function(face){
    var n = faceNormals[face];
    var list = [];
    for (var x=-1;x<=1;x++) for (var y=-1;y<=1;y++) for (var z=-1;z<=1;z++) {
      // find cubie at this grid pos with a sticker facing n
    }
  });
}

Simpler: for each cubie, for each sticker mesh, compute world direction of the sticker normal (mesh.getWorldDirection gives +Z of the plane in world) and world position; collect color per face. Then print for face F: stickers whose world normal ≈ (0,0,1), sorted by x,y.

Implementation: need updateMatrixWorld — the renderer does it each frame.

Let me add that and console.log after each move.

Wait: the debug log prints after each move, and faceColors is defined later in the file but function declarations are hoisted within the IIFE — yes, function declarations hoist ✓.

Also note: the "body" check `child === c.mesh.children[0]` — body is the first child added ✓.

Now reload, enable __DEBUG_FACES via... I can't eval JS. Hmm. window.__DEBUG_FACES must be set true. I'll just always log (remove the flag) temporarily, then remove later. Or set the flag default true and turn it off before finalizing. Let's set it to true temporarily by editing the condition to always log; I'll revert after verification.

Alternatively use the browser console? The tool has no eval. I'll edit the flag to true.

Also the printed grid orientation may be confusing; but I mainly need to confirm F face all green after F move.

Let me set window.__DEBUG_FACES = true at init temporarily.

Solved cube rendering nicely. Now click F (216, 677) and read console STATE.

STATE after F:
- F face: all green (18a558) ✓ correct — F face remains green.
- U: bottom row (last 3 in my ordering) orange f97316 → the U row adjacent to F is orange (from L) ✓ F clockwise: L→U ✓.
- D: first row red dc2626 → D's row adjacent to F is red (from R) ✓ R→D ✓.
- R: right column white f4f5f7 → R's column adjacent to F is white (from U) ✓ U→R ✓.
- L: middle+right column orange, left column yellow → L's column adjacent to F (the front column of L) should be yellow (from D) ✓ (L grid ordering: for L I used ax = -z; the left column is z=+1 → front column yellow ✓).
- B: all blue ✓.

All consistent with standard F clockwise. The rendering I misread earlier was actually showing the F face as green with white in the right column — wait the screenshot shows white column on the F face's right column?! But STATE says F is all green. Hmm, in the screenshot, the right column of the left face shows white cells — but that column might be the R face's front column (the image's center edge). Indeed the R face (right) has its left column white ✓ (STATE R: white in right column of my ordering = the front column ✓). And the image: white column adjacent to the vertical edge is on the red face? Looking at the image, the white column at x≈620-690 appears left of the red face region... The cube's front-right edge is at x≈620. Hmm.

Look at the image again: The green face spans x≈370-620. The red face spans x≈620-800. There's a white vertical column at x≈620-690 which is inside the red face region — that's the R face's front column = white ✓. And at the top there's yellow (U front row should be orange, hmm the top shows yellow at front row, middle-right?).

Top face in image: rows: back row white(3), middle row white white yellow?, front row white yellow yellow? My U grid ordering: key = (ay+1)*3+(ax+1) with ay = z (for U), so index 0..2 is z=-1 row (back), 6..8 is z=+1 (front). U = white×6 then orange×3 → front row orange ✓. In the image the front row of the top face shows yellow/yellow at positions... The image shows yellow cells in the middle-ish of the top face, which could be the front row partially (perspective). The orange f97316 looks yellowish-orange in the render — indeed f97316 is orange but appears yellowish under bright lighting? The rendered color looks yellow (like f2c40e). Hmm, the top face's front row: I see one cell that looks orange-yellow and one bright yellow.

Whatever — the pixel colors may be washed out by lighting/sRGB. The important thing: the logic is verified numerically. But the render shows the front row of the top face as yellow rather than orange... The D face's front row is red ✓ (per state). Hmm.

Possible cause: my debug grid mapping for U uses ay = round(p.z) and for the D face ay = -z. Whatever.

Let me instead double check the render visually for a distinctive case later. Actually there is one thing to verify: the sticker on the U face front row in the render appears yellow (f2c40e = yellow) not orange. But the state says U front row = f97316 (orange). If the render shows yellow there, then the sticker colors in the render don't match... but colors are per-mesh materials; the state reads the same materials. So they must match. It's likely my perception of the screenshot; the "orange" f97316 might render as a yellow-orange due to tone mapping? f97316 is orange; in the image, the D face front row would be red and there's red at the bottom. Hmm.

Wait, look at the image: on the top face, the front row: cell1 (left, at x≈540) appears bright yellow, cell2 (x≈610) yellow, cell3? Actually there are 2-3 yellowish cells. And the green face has white in its... hmm, at the top of the green face near the top edge there's a white cell at (540,290)?

I think the image is showing: U front row = orange (rendered as yellowish-orange). Fine.

Good — the numerics confirm correct behavior. The earlier confusion was misreading perspective.

Now let's do a final verification of the requested check: turn a face and apply its inverse → stickers return to starting arrangement. Do it with the state output: click F, then F', and compare STATE with the initial solved STATE. Let me capture: initial STATE wasn't logged (only after moves). After F' the state should be solved: U all white, D all yellow, F all green, B all blue, R all red, L all orange.

Also test D, L, B via buttons quickly to make sure no errors (they use the same code path). Clicking D (216,560) and B (142,735) etc. Let me do a batch: click D, then L, then B', then check the state is a valid permutation (each face has 9 stickers, all colors preserved). A simpler invariant: total sticker colors unchanged. I could add a check in the debug output but the STATE already lists all 54 stickers.

Let me click F' now (67, 735) and verify solved state.

The STATE after F' is fully solved: U all white, D all yellow, F all green, B all blue, R all red, L all orange ✓. And status "Solved" ✓. Excellent — turn + inverse restores stickers exactly.

Note the screenshot shows the cube mid-animation of F' (the F layer tilted) — that's just the capture timing.

Now let me also quickly exercise D, L, B buttons to ensure no errors (all faces' code path is the same, but let's do one: click D (216,560) and L (142,625) and B (142,735)). Then Reset.

Also remove/keep debug logging? Console logs of a big JSON on each move is noisy. I'll disable it by default (set the flag check to a constant false) but keep the function available. Let me change the condition to `if (window.__DEBUG_FACES === true)` so no logging by default, and expose window.__cube.faceColors for manual checks.

Let me do the D/L/B clicks first.

D move state: F row0 orange, B row0 red, R row0 green, L row0 blue, D all yellow ✓, U all white ✓.

Wait: D clockwise (viewed from below) should move F→R? Let's check standard: D rotates bottom layer as seen from below: F→R? Standard D: F→L? Hmm. Let me derive: clockwise viewed from below = -90° about the D face normal (-Y) = +90° about +Y. Rotation +90 about +Y maps (x,z)→(x cos90 + z sin90, -x sin90 + z cos90) = (z, -x). Point on F (z=1, x=0) → (1, 0) = R. So F→R. But the state shows F's bottom row = orange (L color) and R's bottom row = green (F color)? Hmm — my grid ordering for the side faces: for F, key=(ay+1)*3+(ax+1) with ay=round(p.y): index 0..2 is y=-1 (bottom row), 6..8 is y=+1 (top). So F row index 0-2 = bottom row = orange → the F bottom row shows orange (L). And R's index 0-2 = bottom row = green (F). So F→R ✓ (F's bottom row went to R's bottom row). ✓ Consistent with F→R.

Also B row0 (bottom) = red (R→B) ✓ and L row0 = blue (B→L) ✓. So the cycle F→R→B→L→F for D clockwise. Is that standard? D clockwise viewed from below: hmm. Let's verify with the standard convention: D is clockwise when looking at the D face from below (outside). When looking from below at the D face, the F face appears... Let me set up: viewer below, looking up along +Y. Their "up" direction in view is typically -Z? Arbitrary. But the standard is well-defined: D moves the bottom layer in the same rotational sense as R viewed along the axis...

Let's use the known relation: D = F' R' ... hmm. Use known sequence: R U R' U' = "sexy move". Alternatively use the standard fact: D turn moves the front bottom row to the left? Think of the cube from the front: after D, the front-bottom stickers go to the LEFT face (like a U turn at the bottom) or to the RIGHT?

Standard cube notation: D (clockwise looking at the D face from outside/below). Imagine holding the cube and looking at the bottom. The front face is at the "top" of your view when you look at the bottom? If you tip the cube so the bottom faces you, the front face goes to the top of your view. Then clockwise in that view moves the top (F) to the right (which, in the tipped view, the right side corresponds to the cube's... when tipping the cube backward (bottom toward you), the cube's left-right stays: the right side of your view = the cube's right = R face). Hmm: tipping the cube so the bottom faces you means rotating the cube about the horizontal left-right axis (x-axis) by -90°? Then the front face (F, +Z) rotates to point up (+Y) → appears at the top of your view ✓, and the cube's R face (+X) stays on the right of the view ✓ (rotation about x-axis doesn't change x). So clockwise in this view: top (F) → right (R). So F→R ✓. Great, matches my implementation.

Everything is consistent. Now D' would reverse.

Now L and B buttons — same code path (sign -1). Quick sanity: click L (142, 625) and B (142, 735) then reset; ensure no errors and valid states.

Actually I've validated the uniform rule with U, R, F, D. L and B use the identical formula with sign=-1, and D (sign=-1) verified. Good enough. But let me click them anyway quickly to ensure no runtime errors (e.g., layer selection for x=-1 works).

Let me click L then B in quick succession (queueing tests the queue too).

Hmm, the state after L shows something odd in U/D grids: e.g. U = [red, white, white, blue, white, white, blue, white, white]. Wait, after L, only the L layer changes; the U face's left column should change (U left column ↔ F left column? L clockwise: U→F→D→B→U? Let's check standard L: clockwise viewed from left (-X): the cycle is U→F→D→B→U? L clockwise moves the front-left column down? Standard L: U→B? Hmm.

Anyway the state shows U's left column changed to [red, blue, blue] and D's left column [green, green, orange]. Hmm, but wait — the previous state (after D) already had U entirely white, D all yellow, F bottom row orange, etc. After L, U's column 0 = [red, blue, blue]?? Those come from B's column (red/blue?) hmm B before L = [red,red,red,blue,blue,blue,blue,blue,blue] → B's right column? For B I set ax = -x, so B index 0..2 = x=+1 column (the R side) = red. L turn brings B→U? So U's x=-1 column ← B's ... whatever.

Hmm, but wait: U's column0 entries [red, blue, blue] — that matches B's column at x=-1 being [red, blue, blue]: B's x=-1 column is index 6..8 = [blue,blue,blue]. Hmm not matching. B column x=+1 = red,red,red.

Let's compute: L (sign=-1, x axis), angle = +1 * (-1) * 90 = -90 about +X? Wait formula: angle = (inverse?1:-1)*sign*(PI/2) = 1 * (-1) * PI/2 = -PI/2 about +X. So L = -90° about +X = same as R's rotation but on the left layer. Rotation -90 about X: U→B, B→D, D→F, F→U. So for the L layer: U's left column → B, B's left column → D, D's left column → F, F's left column → U.

Check: U's left column ← F's left column. F before L: [orange,orange,orange, green×6] with my F ordering: index0..2 = bottom row (y=-1), 3..5 middle, 6..8 top. F's left column (x=-1) = indices 0,3,6 = [orange, green, green]. But U's left column became [red, blue, blue]... doesn't match!

Hmm. So maybe my assumed rotation direction for L differs. Let me recompute what U column0 = [red, blue, blue] came from: B before L = [red,red,red,blue,blue,blue,blue,blue,blue]: B's left column (x=-1) = indices 6,7,8 = [blue,blue,blue]. R before L = [green,green,green,red×6]: R's left column (z=+1, front) = indices 0,3,6? For R I used ax = round(p.z), key=(ay+1)*3+(ax+1) → index0..2 = z=-1 (back), 6..8 = z=+1 (front). R's z=+1 column = indices 6,7,8 = [red,red,red].

U column0 = [red, blue, blue] where index 0..2 = z=-1..? For U, ay = round(p.z), so U index 0..2 = z=-1 (back row), index 6..8 = z=+1 (front row). So U's "column 0" is x=-1 across rows z=-1,0,1: values [red, blue, blue].

Hmm what face has [red, blue, blue] in a column? R's z=+1 column = [red, red, red]. B's x=-1 column = [blue,blue,blue]. Mixed [red,blue,blue]?? That's not a single face column — that's suspicious! It suggests the state isn't a proper cube move?!

Hold on. My debug grid mapping may be buggy (e.g., using round(p.z) for positions after rotation is fine since stickers are at cubie positions ±1). But mixed values within a column would mean the sticker colors in a world-face column come from different faces — impossible for a real move.

Unless... the "column" I compute is not a real column due to my key mapping for U: For U I used key = (ay+1)*3 + (ax+1) with ay = round(p.z) — but the U face grid should be indexed by x and z, and rows along z. Row index = z, column = x. So index0..2 = z=-1 row, columns x=-1,0,1. Then "column 0" = indices 0,3,6 = (x=-1, z=-1), (x=-1,z=0), (x=-1,z=1) — that's a column along z ✓ values [red, blue, blue] still mixed.

Hmm, so a real column at x=-1 on the U face has colors red, blue, blue? For the L move, U's x=-1 column gets F's x=-1 column (if U←F) or B's column (if U←B).

Before L: F = [orange,orange,orange, green,green,green, green,green,green]: F's x=-1 column = indices 0,3,6 = [orange, green, green]. B = [red,red,red,blue,blue,blue,blue,blue,blue]: B's x=-1 column = indices 6,7,8 = [blue,blue,blue].

U after L = [red, white,white, blue,white,white, blue,white,white] → column0 (indices 0,3,6) = [red, blue, blue].

Neither [orange,green,green] nor [blue,blue,blue]. So something IS off!

Hmm wait, but maybe my column extraction is wrong because for U I set ay = p.z but for a face at y=+1 the stickers' positions... let me reconsider: after L, the U face stickers are at y=+1 (positions of cubies). p is the sticker's world position: for a sticker on the U face of a cubie at (x, 1, z), p = (x, 1.008, z). round(p.z) = z ✓, round(p.x) = x ✓. So key = (z+1)*3 + (x+1). Index 0 = (x=-1,z=-1), 1 = (x=0,z=-1), 2=(x=1,z=-1), 3=(x=-1,z=0)...

So the entries at indices 0,3,6 = x=-1 column: [red, blue, blue].

For a valid cube state, the U face's x=-1 column (the left column of the top face) after one L move should contain either all three F-left-column colors or all three B-left-column colors. Getting [red,blue,blue] means mixed.

Unless the L turn was applied to the wrong layer set, or the ordering of colors is scrambled incorrectly...

Hmm, hold on: maybe my debug function is misreading because multiple stickers map to the same key and overwrite each other (last wins), while some key has no sticker (remains '?'). But all 9 keys are filled with values, no '?'.

Wait, actually there's a subtle issue: after a move, a sticker that was on the U face of a cubie in the L layer moves to the B face of that cubie, and the sticker that was on the F face moves to U. The colors on the U face's x=-1 column should all be from the F face's x=-1 column (if the move maps F→U) = [orange, green, green] (from before-L F). Hmm, but the F face before L was [orange,orange,orange,green×6] which came from the D move: D put F's bottom row = orange. F's x=-1 column = (x=-1,y=-1)=orange, (x=-1,y=0)=green, (x=-1,y=1)=green.

But we got [red,blue,blue] for U's x=-1 column. Red and blue are from B and R... so the values came from a different source entirely.

Hmm! Maybe my assumption about which cubies are in the L layer is wrong! L layer = cubies with x = -1. Yes.

Wait... maybe the bug: after the D move, the L-layer cubies... no.

Let me reconsider: maybe my debug mapping for U is wrong because after the L move, the stickers facing +Y are at positions... hmm, the U stickers (facing +Y) belong to cubies in the top layer (y=1) — but wait! After moves, the cube's structure: the cubie positions are a permutation of grid slots, so a cubie at position (x=-1,y=1,z) may hold a sticker facing +Y. Yes.

But here's the catch: for a cubie at slot (x, 1, z), the sticker facing +Y is at p=(x, 1.008, z) — unless the cubie's local +Y doesn't point to world +Y... but then the sticker wouldn't face +Y and wouldn't be counted. But there could be a sticker at slot (x,1,z) facing +Y while the cubie's position is (x,1,z)... fine.

Hmm, so the color at U[x=-1,z=-1] = red. Which sticker faces +Y at slot (-1,1,-1)? Its color is red (R color). Plausible after L: the R face's stickers moved to... wait, R stickers (red) are on cubies at x=+1 originally. For a red sticker to be at slot x=-1, the cubie must have moved from x=+1 to x=-1 — impossible in an L move (L only affects x=-1 layer)!

Unless... the D move before moved things, but D affects y=-1 layer only; a red sticker could be at the bottom layer. After D, the R face's bottom row became green (F→R) and L's bottom row blue. So red stickers exist at R face rows (not bottom) → at x=+1.

So a red sticker facing +Y at slot x=-1 means the move moved an R-layer cubie to x=-1?? That contradicts L.

Unless the "L" click actually applied a different move! The status log says "F F' D L" ✓ L applied.

Hmm, but wait: maybe my debug function has a bug in the "best" face determination: I use child.getWorldDirection(n) which returns the object's +Z axis in world space. For a sticker plane rotated to face -X etc., its +Z points along the face normal ✓. But for a sticker on a cubie face that was rotated by a cube turn, the sticker plane's +Z rotates with the cubie ✓.

But `bestDot = 0.8` threshold and `best` chosen by max dot ✓.

Hmm, but here's a catch: the body mesh (BoxGeometry) is children[0] and I skip it via `child === c.mesh.children[0]` ✓ — but wait, in buildCube I add the body first then stickers ✓. However in the debug function I check `if (!child.material || !child.material.color) return;` — the body has a material with color 0x0d1117! And the body IS children[0] so skipped ✓. But hmm — `c.mesh.children[0]` — after a move, I re-parent the cubie mesh; children order preserved ✓.

So the body is skipped, and the stickers counted: 54 stickers → but each face got 9 entries filled ✓ (no '?').

So the count of 54 stickers is right, but colors are mixed in a column. That means my computation of the world direction or position is off... OR the cube state itself is wrong!

Hmm, but the F then F' test gave a perfectly solved state, and D gave consistent rows. So the moves are mostly right.

Let me recheck the L state more carefully. After D (state): U all white, D all yellow, F=[orange×3 (bottom row), green×6], B=[red×3 (bottom row), blue×6], R=[green×3 (bottom row), red×6], L=[blue×3 (bottom row), orange×6].

After L, expected (if L cycles U→B→D→F→U, i.e. U←F):
U's x=-1 column ← F's x=-1 column = [orange, green, green]
B's x=-1 column ← U's x=-1 column = [white,white,white]
D's x=-1 column ← B's x=-1 column = [blue,blue,blue]
F's x=-1 column ← D's x=-1 column = [yellow,yellow,yellow]

Observed after L:
U = [red, white, white, blue, white, white, blue, white, white] → x=-1 column = [red, blue, blue]; x=0 column = [white,white,white]; x=+1 column = [white,white,white].
D = [green, yellow, yellow, green, yellow, yellow, orange, yellow, yellow] → x=-1 column = [green, green, orange]; others yellow.
F = [white, orange, orange, white, green, green, white, green, green] → x=-1 column = [white, white, white]; x=0 = [orange, green, green]; x=+1 = [orange,green,green].
B = [red,red,yellow, blue,blue,yellow, blue,blue,yellow] → x=+1 column = [red,blue,blue]; x=-1 column (indices 6,7,8) = [blue,blue,yellow].
R = [green,green,green, red,red,red, red,red,red] → z=+1 column (indices 6,7,8) = [red,red,red]; z=-1 column = green×3.
L = [orange,orange,blue, orange,orange,blue, orange,orange,blue] → my L mapping ax = -z: index0..2 = z=+1 (front) column = [orange,orange,blue]; index 6..8 = z=-1 (back) column = [orange,orange,blue].

Observed U x=-1 column = [red, blue, blue] and B x=+1 column = [red, blue, blue]. Both columns have the same multiset — consistent with a single column moving from B to U?? B's x=+1 column before L was [red,red,red] (bottom row) + [blue,blue,blue] (rows above) = [red,blue,blue]! YES: B's x=+1 column before L = bottom cell red (from D move, R→B) and the two above blue = [red, blue, blue] ✓✓.

So U's x=-1 column after L = B's x=+1 column before L. And F's x=-1 column after L = white,white,white (from U ✓ but U's x=-1 column was white,white,white ✓ since U was all white). And D's x=-1 column after L = [green, green, orange]: B's x=-1 column before L = [blue,blue,blue]? No, observed [green,green,orange]. Hmm.

Let's think in terms of rotation about the X axis: a rotation about X maps slot (x, y, z) → (x, y', z'). For -90 about X: (y,z) → (z, -y). So slot (-1, 1, z) [top] → (-1, z, -1)? Let me recompute: point p=(x,y,z), rotate -90 about X: y' = y cos(-90) - z sin(-90) = 0*y + z = z; z' = y sin(-90) + z cos(-90) = -y. So (x,y,z) → (x, z, -y).

Top layer slot (-1, 1, z) → (-1, z, -1). So U's column x=-1 (slots (-1,1,-1),(-1,1,0),(-1,1,1)) maps to slots (-1,-1,-1), (-1,0,-1), (-1,1,-1): i.e., B's column x=-1 (z=-1). So U→B ✓ (matches my earlier cycle U→B, B→D, D→F, F→U).

Now B's x=-1 column before L = slots (-1,y,-1) for y=-1,0,1: B colors: index for B: ax = -x → key=(ay+1)*3+(ax+1) with ax=-x. Slot (-1,y,-1): x=-1 → ax=1 → key=(y+1)*3+2 → indices 2,5,8 → B = [red,red,red,blue,blue,blue,blue,blue,blue] → index2=red, index5=blue, index8=blue → [red, blue, blue] ✓ That's exactly U's x=-1 column after L? Wait no: U→B means B's column receives U's stickers, and F→U means U's column receives F's stickers.

Hold on, the rotation maps slots; a sticker at slot s moves to slot R(s). F's column x=-1, z=+1: slots (-1,y,1) → (-1, 1, -y): i.e., F's front column maps to U's back column (z=-1)! Not U's x=-1 column of varying z.

Ah, I conflated: a rotation about X maps the F face plane (z=1) to the U face plane (y=1), and the F face's x=-1 column (varying y) maps to U's x=-1 row (varying z). So the stickers arriving on U's x=-1 column (varying z) come from the F face's varying... let's see: U slot (-1,1,z) has preimage: inverse rotation (+90 about X): (x,y,z)→(x, -z, y). So slot (-1,1,z) ← (-1, -z, 1): i.e. F face slots with x=-1, z=1, y=-z. So U's x=-1 column (varying z) ← F's x=-1 column (varying y) = [orange (y=-1), green, green] as z varies...

Hmm, so U's x=-1 column should be [orange, green, green] (in some z order), not [red,blue,blue].

But observed [red,blue,blue] = B's x=-1 column (which I computed as indices 2,5,8 = red,blue,blue)...

Hmm interesting: B's x=-1 column = [red, blue, blue] too. And U's x=-1 column after L = [red, blue, blue]. So the U column received the stickers that were on B's x=-1 column?! But rotation about X can't move B→U... unless the rotation is +90 about X instead of -90.

+90 about X: (x,y,z)→(x,-z,y). Then B slot (-1,y,-1) → (-1, 1, y): B's x=-1 column → U's x=-1 column ✓✓ MATCHES!

So L applied +90 about X (not -90). Which means L behaves like the inverse of what I intended? Let's check: with angle = +90 about +X for L... my formula: angle = (inv?1:-1)*sign*PI/2 with sign=-1 → -PI/2 for non-inverse. So L = -90 about +X. But the observed is +90 about +X.

Hmm wait, but the mapping direction: with -90 rotation, a sticker at slot s moves to R(s). I computed R(-90): (x,y,z)→(x,z,-y). So B slot (-1,y,-1) → (-1,-1,-y) = D face. So B→D. And F(-1,y,1) → (-1,1,-y) = U. So F→U.

Observed: U's x=-1 column got B's x=-1 column colors → so B→U, meaning the rotation was +90 about X: (x,y,z)→(x,-z,y): B(-1,y,-1)→(-1,1,y) = U ✓ and F(-1,y,1)→(-1,-1,y) = D.

Let me check F's x=-1 column after L: observed [white,white,white] = U's x=-1 column before L (white) → U→F ✓ consistent with +90 about X.

And D's x=-1 column after L observed [green, green, orange]: preimage with +90: D slot (-1,-1,z) ← inverse (-90): (x,y,z)→(x,z,-y) → (-1, z, 1) = F face x=-1 column = [orange, green, green] ✓ (order varies) ✓.

Great, so L applied +90 about X. But my formula gives -90 for L...

Let me recompute my formula. angle = (mv.inverse ? 1 : -1) * sign * (Math.PI / 2). For L: sign = SIGN['L'] = -1, inverse false → (-1)*(-1)*(PI/2) = +PI/2 = +90 about +X.

I made an arithmetic error earlier. So L = +90 about +X. Now is that correct for L clockwise? L clockwise = -90 about the L face normal (-X) = +90 about +X ✓. And the observed behavior = +90 about +X ✓ CORRECT!

Great, so my earlier reasoning about "U→B→D→F" for L was wrong; the actual L (clockwise from outside) is: F→D, D→B, B→U, U→F? Let's verify with the standard: L clockwise moves the U left column → F left column ✓ (that's what we observed: U's white column → F). Yes! Standard L: the left column of U goes to the front (L moves the top-left column toward the front). ✓ Correct.

And D move: we verified F→R for D ✓ (standard D: the bottom front row moves to the right) ✓.

And B (sign=-1, z axis): angle = -1 * -1 * PI/2 = +90 about +Z. B clockwise = -90 about B normal (-Z) = +90 about +Z ✓.

Great — all correct. My earlier confusion about the formula was arithmetic; the implementation is right.

Everything checks out. Now:
1. Remove the debug console logging (make it opt-in).
2. Also double check the `moved` variable is unused — fine, but I could use it to distinguish click vs drag (not needed).
3. Consider: pointerdown on the canvas also happens when clicking buttons? No, buttons are separate elements.

One more consideration: the requirement "Dragging the background orbits the camera without turning a face." ✓ (no face dragging at all).

Also "bounded wheel zoom" ✓ 5–14.

Let me now disable the debug logging, and also expose faceColors in __cube. Then do a final reload + verification pass: screenshot solved, click U then U', status Solved; drag to orbit; reset; screenshot.

Also I might reduce the debug function's presence — keep it, it's small and off by default.

Let me edit the log condition to only log when window.__DEBUG_FACES === true.

Clean solved state, no console errors.

Final check sequence as required: turn a face + inverse, orbit, reset. Already done individually, but let's do a final quick pass in one go:
1. Click U (67,560), wait, click U' (142,560) → status Solved.
2. Drag to orbit → camera changes, no face turn.
3. Click Reset → solved + initial framing.

Let me run steps 1 quickly.

U turn: F top row = red (R→F ✓), R top row = blue (B→R ✓). Correct.

Now click U' (142,560) → should return to solved.

The screenshot was captured mid-animation of U' (top layer tilted), but status already says "Solved" and log "U U'". The screenshot timing vs status update: the status updates after the animation completes, so the render captured is one frame earlier? Actually the render loop draws continuously; the status update happened in the rAF step that finished the animation — the screenshot might be from the frame right before. Let's take another screenshot to confirm the final solved visual.

Solved again after U + U' ✓ (identical to the starting arrangement).

Now final: orbit via drag (background) then Reset → check framing.

Orbit works — camera moved (now viewing F from a lower/front angle, L and D visible). No face turn occurred (still Solved, log unchanged) ✓.

Now click Reset → should restore initial framing and solved state.

Reset restores the solved cube and the initial camera framing (identical to the first screenshot) ✓.

One more scenario worth checking: Reset while a scramble is mid-animation (abort path). Let's test: click Scramble, then immediately click Reset, and verify the cube is solved and no errors.

Also keyboard shortcuts. Let's do that test quickly.

Reset mid-scramble aborts cleanly: solved cube, no console errors, initial framing ✓.

Final touch-ups:
- The "Scramble" button's random sequence should probably avoid repeating the same face consecutively — done.
- The `moved` variable unused — harmless.

One thing: the sticker gaps show a bluish-gray body color (looks slate). It renders as visible cubie boundaries ✓.

Let me double-check that the cube is fully visible at initial framing — yes, the entire cube fits within the viewport.

Also check the file is self-contained: only reference is three.min.js local script ✓. No network.

Let me do a final grep for http/CDN references in index.html and confirm the file size, and validate that there's only one script tag referencing three.min.js.

No external references. The 3 "script" matches: `<script src="three.min.js">`, `<script>` and `</script>`.

Done. Let me write the final report.