The closure walk at capacity R =

Every lattice point of ℤ⁴ within ℓ¹-distance R of the origin, joined by the eight twists. Edge colour is the ℤ₂ connection; a closed path's Pauli phase is the product of its edge signs.

Show gauge-axis nodes (x₄ ≠ 0) edges with connection +1 edges with connection −1 shade the π-flux plaquettes slow rotation

Key

origin — the closure set

|x|₁ = 1 2 3

node with gauge component

connection +1

connection −1 (Jordan–Wigner sign)

Spatial axes X, Y, Z are drawn as three orthogonal directions; the gauge axis is the fourth, drawn as a skew offset. Drag to rotate, wheel to zoom, hover a node for its ways-to-close counts h(x,t). Spec: Closure_Walk.md §3; built and checked by closure_graph.py.