Knowing quite a bit about sundials I was genuinely curious about how that would work, as a typical (horizontal) sundial doesn't have enough information to make a calendar. It's a time of day device, rather than a time of year device. You could teach the model about the Equation of Time or the Sun's declination, but it wouldn't need the sundial at that point. There are sundials like a spider sundial, or nodus sundial, that encode date information too. But there's overlap/ambiguity between the two solstices as the sun goes from highest to lowest, then back to its highest declination. Leap years also add some challenges too. There are various ways to deal with those, but I think you can see why I was curious how producing a calendar from a sundial would work (without giving it some other information that makes the sundial unecessary).