St. Tib's Day is the day inserted into the Discordian Calendar every 4 years between Chaos 59 and Chaos 60. Though the Principia says that the day occurs once every 4 years, it first says that the Discordian and Gregorian calendars are perpetually aligned. Thus, we can reason that we actually only insert St. Tib's Day into every 4th year that does not end in 66, unless that year's century is 3 more than a multiple of 4. For example, 3166 does contain a St. Tib's Day, but 3066 didn't and 3266 won't.
Some may believe that the "once every 4 years" rule has precedence, which means the Discordian Calendar is actually aligned to the Julian calendar, but they are horribly mistaken.
So say I, Pope Max Flax Beeblewax, speaking ex cathedra, on this the 71st day of Confusion in the 3171st Year of Our Lady.