This is the genuine 2D Fibonacci string-net code: a real Levin-Wen topological code with quantum dimension d_τ = φ, on a torus with a true logical qubit, not a 1D τ-chain surrogate and not the older Fibonacci-concatenated-surface construction.

The fair head-to-head is the gold vs red curves: Fibonacci (d=φ) against the Z₂ toric code, which is the surface code's topological order, run on identical machinery: same lattice, same dephasing noise, same projective syndrome, same minimum-weight decoder, same entanglement-fidelity metric, same distance-4 code. There is no asymmetry to rig. The only thing that differs between the two curves is the F-symbol that makes the code Fibonacci. On this fair axis, Fibonacci is competitive, consistently a touch better.

The blue dashed curve is the literal surface code (SurfaceQEC, union-find on the planar lattice) as an independent anchor. It uses a different metric (a single-qubit binary logical-error rate, not the 2-qubit entanglement fidelity of the gold/red pair), so its absolute height is not directly comparable; it is shown only to confirm the red leg sits in the standard surface-code regime.

Scope (no overclaiming): this is a fair comparison point at a single distance under code-capacity noise, not a threshold curve. A multi-distance threshold needs the tensor-network decoder (the boundary-MPS contraction engine is built and validated against exact contraction; the Levin-Wen PEPS + TN decoder is the scoped next step). Everything here is computed live in your browser from phi-quantum-stringnet-cpp via WebAssembly.