2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228187Recently, using supergravity analysis, a hyperbolic reflection group was found to underlie the structure of wall-crossing, or the discontinuous moduli dependence of the supersymmetric index due to the presence of walls of marginal stability, of the BPS dyons in the N=4, d=4 compactification. In this paper we work in the regime where four-dimensional gravity decouples and we show how the presence of such a group structure can be easily understood as a consequence of the supersymmetry of a system of (p,q) five-brane network, or equivalently the holomorphicity of the Riemann surface wrapped by the appropriate M5 branes in the Euclidean M-theory frame.37 pages, 5 figuresHigh Energy Physics - Theorytext