Proleptic Julian calendar
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The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for details.
A calendar obtained by extension earlier in time than its invention or implementation is called the "proleptic" version of the calendar, and thus we obtain the proleptic Julian calendar. Likewise, the proleptic Gregorian calendar is occasionally used to specify dates before its official introduction in 1582. Because the Julian calendar was actually used before that time, one must explicitly state that a given date is in the proleptic Gregorian calendar when that is used.
Historians since Bede have traditionally represented the years preceding AD 1 as "1 BC", "2 BC", etc. Bede and later Latin writers chose not to place the Latin zero, nulla, between BC and AD years. In this system the year 1 BC would be a leap year. To determine an interval in years across the BC/AD boundary, it is more convenient to include a year zero and represent earlier years as negative. This is the convention used in "astronomical year numbering". In this system the year 0 is equivalent to 1 BC and is a leap year.
Further considerations involve the fact that the Julian calendar isn't much older than AD 1 itself, so simple addition to year numbers from the Roman pre-Julian calendar (Ab urbe condita) aren't necessarily direct conversions. The top example is that the year 46 BC, as a result of the Julian reform that initiated the calendar of that name, was allotted 445 days by Julius Caesar. In years prior to this, the Romans added whole intercalary months in an unsystematized manner. In years between this date and AD 4, the leap day likewise was unsystematic.
