They say they explenation for day-hight cycle
http://www.wildheretic.com/how-is-there-night-and-day/
But notice how just like FE, they try a very superficial explanation. They focus on simply the existence of day and night.
They make no attempt to explain how the sun appears, how the sun appears to set.
If the sun had a light side and a dark side, we would not always observe it as a bright circle, that appears to set below/beyond the horizon.
Instead we would observe it high in the sky, with phases like the moon. At midnight we would see a new Sun. Just after midnight we would wee a waxing crescent sun. At roughly 6 am we would see a 1st quarter sun, and just after it would go to a waxing gibbous sun. Then at midday we would get a full Sun. Then it would start waning, go through the gibbous, quarter and crescent sun phases, until it again reaches a new Sun at midnight.
So that doesn't explain it at all.
If they want to claim it is a disk instead of a sphere, then it is slightly better, but still has massive issues.
You have darkness from it until roughly 6 am, at which point it starts out as a thin line, becoming an ellipse and gradually stretching out into a circle at midday, before getting squished again to a line high in the sky for roughly 6pm.
Yet again, failing to match reality.
Instead it is just a superficial explanation to pretend it is solved, in the hopes that you don't bother actually thinking about it to see if it matches reality.
And they can make accurate predictions.( http://www.wildheretic.com/can-this-theory-make-predictions/ )
The important part is not if they can make accurate predictions, it is if these are based upon their model.
And in the page you linked, they don't predict anything.
Even with a further link to their attempt at an explanation for the sun, they just leave it as magic bendy light.
No justification for light is bending like that, nor any formula to describe the path of the light, nor any formula to determine the sun's apparent position at any time of day based upon their model.
And world leading mathematicans calcualted that if light bended unlike mainstream science says than it will be inpossible to see diffirence just by looking.
You don't need world leading mathematicians to know that.
The simple fact is you can map every single point in 3D space in our universe to many different equivalent ones, including that of a concave Earth and even a cube Earth.
Pretty much anything that is topologically equivalent to a sphere it can be mapped to.
This mapping will require significant distortion, requiring light and even space itself to bend and distort.
Concave offers answers that flat Earth can't and for me, and it is superior to FE form my point of view.
While is is superior, in that it accepts Earth is round, that is about the only superiority.
Neither are based upon any actual evidence.
Neither are backed up by reality.
Both require nature conspiring against them to pretend the model is wrong in almost every way.