We derive the rho meson mass and width from the line graph topology of the 4.8.8 Archimedean lattice. The vector meson mass emerges as the line graph adjacency eigenvalue of the octagonal matter plaquette, automatically satisfying the KSFR low-energy theorem relating the pion decay constant and vector meson mass. The tree-level decay width of 137 MeV agrees with experiment to -7.9%, leaving exactly the room expected for NLO vertex corrections. The topological duality between electroweak symmetry breaking (golden to silver ratio) and colour confinement (silver to golden ratio) reveals that mesons are the unhealed topological scars of the strong interaction.

Part of the Holographic Circlette paper series. See the summary paper (Part 22) for an overview of all results.