Urbis13
Mapped. Actually the situation it is less complicated than seems. The parking spaces in the square are divided in two zones: parking places near the south building and parking place in the middle of the square ("zona centrale" -> "central zone"). If you park in the first group of parking places you can park freely but you can stay only 1 hour; if you park in the others you have to pay (from the beginning of the parking time). These conditions apply only from 08:00  to 20:00 (during other times parking is free and unlimited).
Probably the design of the road sign it is not the clearest but tolled parkings use blue markings in Italy (so the situation it is make more understable by them)