Reading back over some of the recent back and forth, you may not fully appreciate what a solar term was legally and culturally, and why we have a pretty good idea how they were defined, not just abstractly, but like
how.
The calendar is a few things, but first and foremost it sets when the Emperor is going to do certain rituals to align Heaven and Earth. The foreign dynasties were never exactly welcomed, but even they pretty quickly adopted these practices in order to assure the Han people that they were going to maintain the relationship between Heaven and Earth. Like any durable premodern state religion, this also has practical dimensions. The obvious one is that it means all Imperial correspondences are correctly dated and the bureaucracy is standardized. The agricultural calendar is important for the state function of storing grain against famine, and while important guidance for any crop, vital in rice growing areas because local officials coordinated the flooding and draining of rice paddies. So it is definitely a metaphysical thing, but the calendar is also a practical timekeeping device based on the Heavens and a literal tool for ordering the relationship with the literal Earth.
The consequence of this is that for most purposes a solar term is whatever the government with Mandate of Heaven says it is. This logic goes both ways; publishing a competing set of solar terms is to declare yourself to be the rightful interpreter of Heaven and make a bid for the Mandate. This is one of the first things a rebel dynasty issued---often with nearly the same calendar, but the new Emperor's name slapped on it. Private astronomy is not unheard of, but it was a very delicate thing to undertake and you certainly weren't going to imply that the Emperor was doing important rituals in the wrong month unless you were ready to back that with an army and a candidate to do them right. Exactly how touch private astronomy was waxed and waned a bit, but there was no era where you could safely put down a plain revision to the calendar. In the context of the VMS, the Ming were especially jealous of their rights to do this kind of astronomy under the Mandate, so a 1420s date looks very strange for this kind of speculation.
An astrologer in particular has no business checking the work of the Astronomical Bureau. First of all, it's just hard to do that kind of
astronomy without building the huge gnomons and water clocks that the state was using. But more importantly no one wants an astrologer who is recommending dates that go against the plain will of Heaven. If the Emperor's solar terms were wrong, the dynasty would fail; the calendar is obviously aligned with Heaven. And if your astrologer didn't have access to an official calendar, there were no auspicious dates---metaphysically because those come from the Emperor's relationship with Heaven, but more pragmatically because of the ongoing war and looming famine. The fact that it would be one of the most serious capital offenses to circulate a competing definition of solar terms really breaks the plausibility of all this for me.
Bear in mind as well that the problem of
observing the solar terms was very nearly solved. You need a very big gnomon, sophisticated math, and trained astronomers to bring those two things together, but they got to the Gregorian estimate of the tropical year 300 years before Europeans did, so they were finding these moments to a high degree of accuracy. You can increase the accuracy further, but the practical error was already tiny. The problem is that about when you
observe Dahan, your officials expect to be getting the calendar with the Dahan that is a full tropical year away. Further, the observation method and and computations are totally thrown off if there are cloudy days around the term, and that's a real problem for some of them. What was needed was a way to reliably
predict the solar terms because legitimacy came from the calendrical, not astronomical, function. As a modern who can Google You are not allowed to view links.
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Login to view. and see that the mean-time solar terms can accumulate over 4 days of error in the fall, this seems to me like an absurd compromise, but I can also solve the Keplerian problem for time with relative ease, especially if I'm allowed to use my computer. The solution required a 20 year project of translation, education, and international cooperation to get The Astronomical Bureau to that point in 1645, and it was based on science that was only a few decades old in Europe. I don't see how bringing in stellar astronomy makes it any easier to solve the problem that you have to work these dates out in advance for a calendar, especially since stellar astronomy was orders of magnitude less exact.
Chinese history is long, the archives enormous, and much has been lost. But I think you're underestimating how
official solar terms were. If the authorities had wanted to divide the pentads further, they would have circulated that fact widely. If someone else had done it, it would be a capital offense that would have been stamped out, raising questions about who under Heaven was passing it to some travelling white guy. I have obvious theory of knowledge objections to speculating that maybe one day you'll have evidence---that's not how knowing things works!---but I also don't think you appreciate how extraordinary the document you're imagining would be.