What is "gold number"?
A red gold sol is a colloidal suspension of gold nanoparticles with average size of particles less than 100 nm. The suspension is quite stable — the nanoparticles don't aggregate because of the existence of an electrical double layer on the surface of particles which causes electrostatic repulsion between the particles.

If you add a sufficient amount of an electrolyte (e.g., NaCl) to the colloid, the ions will disrupt the electric double layer which will cause aggregation (coagulation) of gold particles. A stabilizing agent (e.g., citric acid) is a compound that is able to adsorb on the surface of gold nanoparticles and protect them from aggregation (it acts like a shield), even in a high electrolyte concentration.