Gnutzmann–Smilansky–Weber quantum-graph nodal-statistics conjecture

Let a quantum graph be a metric graph with edge lengths, and let the nodal domains of an eigenfunction be the connected components of the complement of its zero set. Consider well-connected graphs with incommensurate bond lengths, and the distribution of their nodal-domain counts in the previously specified bounded interval. Gnutzmann–Smilansky–Weber's conjecture. As the number of vertices tends to infinity, this distribution approaches a Gaussian distribution.

This is a universality conjecture for nodal statistics in quantum graphs. The source later proves a related Gaussian limit for a particular family, but does not establish this general formulation.