[prometheus76]

They only state that they took the dates from old records and converted them to Gregorian dates. They do not say what method they used to convert the dates, and as noted here http://www.yukikurete.de/nengo_chronology.htm, old historical Japanese dates are not reliable and cannot be considered astronomically accurate. This whole paper is written assuming the dates in old records correspond to the Gregorian calendar, and that's simply not the case.

The historical Japanese calendar suffered from drift away from seasonal events because the months had either 29 or 30 days in them, but the actual lunar calendar is 29.53... days long. This was a known problem, and they would occasionally add a 13th month to the year to compensate, but this was only done when either the Emperor died, or when the Emperor said to do it (usually to commemorate some significant battle). Both of those situations means that the leap months were not added in a systematic way, so trying to back-calculate dates has errors. Several attempts have been made over the last 75 years by scholars to create conversion tables for this, but they all have errors and can be inaccurate up to 4 weeks.