Since the Crownbreaker Wars, when Thrax brought its armies into the city and usurped the throne, the Crown has limited the number of soldiers allowed in Arx. Each Great House is allowed no more than 100 soldiers, with an additional 100 allowed between all of its vassal Houses. This means that while Grayson may have 100 soldiers, Bisland and Ashford are limited to 50 apiece, and Bisland may opt to only have 40 while allowing Deepwood 10. This division of numbers is determined first by the High Lords for their vassals duchies, and then by the Dukes and Duchesses down through each vassal House.
In addition to this, there are laws that limit the number in each noble's retinue, determined by social rank. A High Lord may have no more than 12 soldiers attending them in the street outside of their kingdom's ward. A Duke may have no more than 6, a Marquis 5, a Count 4, and no more than 3 to a Baron. The noble families of the title holders are customarily permitted half the number of guards, rounded down.
Commoners typically do not have retinues but the cautious (or paranoid) might hire an armsman or mercenary to accompany them on business and they may not have more than 1 in attendance at a time. This is not policed in the Lower Boroughs due to arrivals at the docks and the Iron Guard do issue permits for larger parties to travel from the harbour to their home wards. But strict records are kept of fealties and the number of soldiers already in the city; the staff of the Minister of Defense will know very quickly if people try to sneak more armed men and women than they are allowed.