The "verification des mandats" or "vérification des pouvoirs" was only a standard procedure of the État Généraux, similar to what we would call an inauguration today. It consisted in a formal identification and swearing in of the members of the États Généraux. You have to remember that identifying someone wasn't as easy as it is today (they didn't have a driver's licence with their picture on it), so you had to make sure no impostor was in the midst of the delegates. The First and Second Estates didn't want this procedure to happen altogether, and wanted to be sweared in separately as a sign of respect for the protocol and social hierarchy. On June 10th 1789, the Tiers-État chose to rename their assembly the Commons, as it was meant to represent all members of the nation without distinction. The King chose to act in defiance and back the Aristocracy who wanted to be verified separately from the common people. The "Commons" decided to proceed anyway and begin the roll call without the Aristocrats. A few members of the Clergy chose to join, and by June 17th, the vérification was over. The États Généraux declared, in line with Joseph-Emmanuel Siéyès' theory, that they represented 96% of the population, which was good enough. They declared themselves a "National Assembly". Two days later, the Clergy chose to join in, as they were beginning to understand the way the wind was blowing. The King saw this move as insubordination (it was indeed), and chose to close the Salle des Menus Plaisirs on June 20th, which led the Assembly to meet in the smaller Tennis Court. The members of the National Assembly then took an oath to give a constitution to the nation, which consecrated the separation of the nation from the body of the King, inaugurating the first undeniable phase of the French Revolution.

Ladan Boroumand, « La nation contre le peuple. Le débat sur la vérification commune des mandats aux États généraux de 1789 », Revue française de science politique, vol. 40, no 3, Persée - Portail des revues scientifiques en SHS, 1990, p. 309‑338.

Jean-Clément Martin, Nouvelle histoire de la Révolution française, Paris, Perrin, 2012.