WebGPUで潰す・投げる・切れるソフトボディのいちごケーキ

Build immediately a complete interactive WebGPU site called “Strawberry Cake.” 
Use genuine WebGPU + WGSL, procedural geometry, mouse/touch, and real-time volumetric soft-body physics. No Three.js/Babylon.js, Canvas2D, external assets, video/GIF, or CSS-only deformation.
Visual: premium Korean/Japanese strawberry shortcake—low, wide, rounded, pillow-soft, with pink sponge, cream layers, pale frosting, piped cream, and strawberries. Warm ivory background, soft studio light, edible moist materials.
Layout: top-left “SOFT STUDIES / NO.001” + italic “Strawberry Cake.” Top-right “WEBGPU · LIVE”. Large centered cake. Right controls: Hand/Knife, presets, Firmness, Damping, Drop, Reset, Pause, ¼ speed, Show mesh. Bottom-left: Mass, Volume, Kinetic, Pieces.
Physics: stable XPBD/co-rotational soft body with tetrahedral sim mesh, smooth render mesh, volume preservation, damping, gravity, floor friction, and piece collisions. Cake feels soft/heavy and wobbles after release.
Hand: hold=Press, inward drag=Squeeze, outward drag=Grab, fast release=Throw. Use weighted grabs, smoothed 3D target, pointer velocity and momentum. Cake remains free; cake input overrides orbit.
Knife: procedural 3D knife. Draw a cut line; animate contact→compression→penetration→breakthrough→lift. Deform before splitting; keep seam thin.
Repeated cutting is mandatory: use a dynamic pieces list; every piece stays cuttable. Convert strokes to vertical cut planes, split crossed pieces, create new soft-body/render meshes, transfer deformation/velocity, preserve toppings, keep halves aligned, update Pieces. Support 14+ pieces and multi-piece cuts. No fixed whole/left/right states.
Drop releases all pieces. Reset restores one intact cake and Pieces=1. Use fixed timestep/substeps, DPR≤2, clamp instability, avoid NaNs/GPU errors. Expose window.__cake.
Run locally, test interactions and repeated cutting, and iterate until polished.