The word derives from fas, meaning "that which is permitted," that is, "that which is legitimate in the eyes of the gods." Fasti dies were the days on which business might be transacted without impiety, in contrast to dies nefasti, days on which assemblies and courts could not convene.
The word fasti itself came to denote lists organized by time.
None of these proceedings were in any way archaeological.
Cardinal Farnese assigned the scholars to watch the diggings.
Public business, including the official business of the Roman state, had to be transacted on dies fasti, "allowed days". In addition to the word's general sense, there were fasti that recorded specific kinds of events, such as the fasti triumphales, lists of triumphs celebrated by Roman generals.
The divisions of time used in the fasti were based on the Roman calendar.
There were in fact two different original lists placed under that name to which were added fragments found in 1816-1818, 1872–1878 and a final one from the Tiber river in 1888, unrestored.
All the fragments became CIL I under Fragmenta Quae Dicuntur Capitolini, "Fragments Called Capitolini" and Cetera Quae Supersunt Fragmenta, "Other Remaining Fragments." The unified list states the magistrates for each AUC from the first year of the first king to the death of Augustus.
Peter's in 1540 and Michelangelo was in fact protestingly working on its design also.
The pope was following the widespread convention that prevailed in the Renaissance of ripping up the structures of the past to reuse in building structures they considered even more magnificent.
It has been estimated that the consular lists were in four entablatures several feet high: I covering AUC 1-364; II, 365-461; III, 462-600; IV, 601-745, running to 766 in the margin.