Fractional Quantum Hall Anyon Braiding — Flux-Attachment Phase Integral (2D)

This 2D companion to the 3D fractional-quantum-Hall braiding simulator renders the same Laughlin-quasihole statistics through the composite-fermion flux-attachment picture instead of an orbiting 3D scene. A synthetic Aharonov–Bohm flux line of strength Φ = 2π/m is attached to the fixed quasihole and drawn as a field of tangential arrows; the moving quasiparticle's statistical phase is computed every frame as a genuine numerical line integral ∮A·dl along its real velocity, then compared live against the geometric winding (angle traveled ÷ 2π) tracked by an entirely separate counter. Because the line integral of a thin flux line is a topological invariant, the two independently computed quantities agree to numerical precision regardless of loop radius or braid speed — a direct demonstration of why braiding phase depends only on winding number at filling factor ν = 1/m.