Firstly, where did these records originally come from? Did they materialise out of thin air?And how were these records first produced? What was the understanding that made these 'simple' recrods possible? Certinally not DET!
The Saros (more properly "Chaldean") cycle was recorded by multiple flat earth cosmologists including notably the Chaldeans, Egyptians, Chinese, and Mayans. The understandings were based on observations recorded after many, many years within which, as Jane so thoroughly noted, are several families of Chaldean Cycles occurring or active at any given time. The Mayans had even refined cycles for the solar eclipses, which is a much, much more difficult task. I am unaware of a single prediction for eclipses that has not depended on the Chaldean Cycle and instead uses some form of Newtonian or Keplerian system. Please provide the work for your 3-body system's math, so that it can be critiqued.
The existence of the planet Neptune was not made not by simply looking up records! A mathematical prediction of its position was made based on the works of both Kepler and Newton. When astronomer Johann Gottfried Galle pointed his telescope at the calculated position....the rest is history.
Myth is not spelt h-i-s-t-o-r-y.
Your constant evading of the question, by either the use of smoke screens or in this case deliberately down playing the intellectual achievements of the past is staggering. It either comes from a genuine poor grasp of the subject
Quoting to highlight irony.
You also fail to address what is the core question, how can these accurate predictions be made and shown to be true, if Newton and Kepler and all what they established is not also true?
These predictions were faithfully made by flat earthers for centuries, nay millenia, before the occultists Newton or Kepler ever appeared on the scene.