Graph ↔ Rectangle Holography (v3c)

"Particle on a graph dual to a string on the rectangle" — click nodes or paths to explore the holography map

Schreier Graph (CFT-Side)

First click: node A. Second click: node B.

Rectangle Paths (ADS-Side)

Highlight area under path

Holography map: Given a binary vector (graph node), read left to right — each 1 = step UP, each 0 = step RIGHT. This gives a bijection from graph nodes to lattice paths on the k × (n−k) rectangle.
Graph edges: two nodes are connected if an adjacent transposition (i, i+1) sends one vector to the other.
Complexity = Area: The graph distance (minimum adjacent transpositions) between two nodes equals the area between their corresponding paths. This is the Mann-Whitney U statistic = area between ROC curves.