Build a Rubik's Cube solver

the prompt

/goal Build me a visually stunning, fully functional Rubik's Cube solver that runs entirely in the browser. This is not a cube viewer — it must actually SOLVE the cube. Requirements: 1. A beautiful 3D Rubik's Cube rendered in Three.js — rounded cubelets, PBR-quality materials, soft studio lighting, smooth 60fps rotations. It should look like a product shot, not a programmer-art demo. 2. SCRAMBLE: a button that applies a random legal scramble (animated, standard move notation shown), plus a text input to enter any custom scramble in standard notation (e.g. "R U R' U' F2 D"). 3. SOLVE: implement a real solving algorithm in JavaScript — Kociemba two-phase or a correct layer-by-layer/CFOP implementation. Correctness beats move count, but show the move count and the solution sequence. Do NOT hard-code reversing the scramble — the solver must work from the cube STATE, and must solve a cube scrambled by hand-entered notation it has never seen. 4. Playback: the solution animates move by move with adjustable speed, current move highlighted in the displayed sequence, pause/step controls. 5. Manual mode: let me rotate faces myself by clicking/dragging, then hit SOLVE from whatever mess I made. Run a quick research pass on solver algorithms before coding if needed, then build, then QA: verify with at least 10 random scrambles AND 3 hand-entered scrambles that the cube always reaches the solved state. Deploy live to Vercel. DONE when: the deployed app solves any scramble I type in, animates the solution smoothly, and looks gorgeous doing it. If a scramble fails to solve, keep going — do not stop until solving is bulletproof.

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