Quantum topology matcher pc 1564

I want you to act as a creative technologist and interaction architect. Construct a single-file (index.html) web game based on spatial alignment mechanics.

GAME SPEC:

Title: Quantum Entanglement

Core mechanic: A 3D array of collapsed particle clusters floats in space. Clicking a cluster unfolds its unique 3D geometric matrix.

Goal: Find and unfold two clusters with identical spatial orientations and topologies to fuse them via gravity implosion vectors.

TECH REQUIREMENTS:

Single file: HTML5 with inline styles and vanilla JavaScript leveraging Three.js via CDN.

Rendering: Three.js WebGLRenderer with high-performance buffer geometries.

Physics: Implement smooth quaternion math for rotating clusters via mouse drag. When a match occurs, compute mutual attraction vectors causing an implosion particle effect before mesh destruction.

Design style: Minimalist surrealism. Pure white void background, frosted glass (transmission) cluster materials, and interactive volumetric light trails.