Comet Caesar, with recorded sightings in 44BC, is the oldest known periodic comet. With Bast's hypothesis of 5 orbits averaging 1025 years, the 44BC passage fits in well with the 2012 end date, and just as importantly the 3114BC start date, of the Mayan Long Count calendar. This estimated orbital period differs from the 44BC sighting by only 6 years, or 3 years per thousand year orbit. Given that the periodicy of Halley's comet can vary by 2 years within a 76 year orbit, due to the gravitational influences of the planets, the connection could be precise.
Bast says "Few researchers have paid any importance to the start date of the Long Count calendar. And few have looked into global cataclysms that ancient civilizations were actually capable of predicting".