"After that, Japan calculated its calendar using various Chinese calendar procedures" also from the wikipedia article. This is all just illustrating my point further.

You're assuming the researchers used earthquakes or astronomical events to correlate their date calculations, but they make no such claim. They do not explain their methodology for converting the historical calendar dates into Gregorian dates at all. Why should we give them the benefit of the doubt? They've included their dataset, but they haven't included their methodology for determining the Gregorian dates, yet their whole claim is that the dates are getting earlier and earlier. The line trending down also correlates with Japan converting to the Gregorian calendar in 1868. Why isn't that mentioned in their paper? If their methodology for converting historical dates is faulty or poor, that methodology could also account for the line appearing to move down starting in the mid-1800s.

They should be transparent about it and they weren't, and a lot of people here seem to be willing to just trust them and their methodology, but I can't figure out what's scientific or transparent about that. Isn't peer review supposed to catch and correct these types of issues before publication? And if not, shouldn't they be transparent enough in sharing their methodology that the concerns raised by amateur idiots like myself would be easily addressed, or at least accounted for?

By everything I've read, it should be included as a challenge, and they should be explicit about the method they used to determine the Gregorian dates, because it's not straightforward, nor is there even an agreed-upon method or table to use for conversion, yet their whole claim rests on the verifiability of the dates.

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.

Shouldn't a scientific paper making a specific scientific claim explain their methodology? Why should the audience presume that the method used to calculate the dates matches the implied trend? The calendar issue undermines their entire claim, and we're just supposed to give them the benefit of the doubt and trust that whatever they did was correct? Where's the scientific objectivism in that?