The third variant was used in Arsacid territories at least as early as 48/7 BC.
The Gorpiaios embolimos of the Trasaka reliquary demonstrates that the Macedonian calendar it used followed the Arsacid rather than the Seleucid solar alignment.
However, if this inscription uses the Arsacid Macedonian calendar, its epoch cannot fall in either year.
Since Gorpiaios embolimos is the same month as Ululu II, we may avoid this difficulty by using the corresponding Babylonian years as the candidate epochs: 66/5 BC (= year 182 in the Arsacid era [AE]) and 47/6 BC (= AE 201).
Even if the Arsacid Babylonian year started half a year after the corresponding Arsacid Macedonian year, following the Seleucid precedent, there is no reason to suppose that a spring-based Indian year of the Yavana era followed the same rule.
If the epoch of the era of Azes was 47/6 BC = AE 201, this era was itself was the second centennial of the Arsacid era.
If the era is correctly assigned, it shows that both the Azes and the Kaniska eras began as centennial cycles of the earlier Arsacid and Yavana eras, and that the origins of the Vikrama era again must be sought elsewhere.
A comparison of the single Macedonian intercalary date from Gandhara with Macedonian calendars outside Gandhara has shown that the most likely model used in Gandhara was the Arsacid calendar.
Between the territory controlled by the so-called Northern Wei and Bukhara there were many other territories where descendants of the Arsacids or of people originally coming from Parthia may have decided to live sometime between the early third century and the time when An Tugen's ancestor decided to move to the territory controlled by the Northern Wei.
Kuwabara asserts that one cannot rely on the passage from the Xin Tang shu because to state that the Arsacids were descendants of Huang Di (the Yellow Emperor) is a farfetched opinion of the first order.