“In contrast, the Gregorian Calendar's strict adherence to the solar cycle produces an expiring calendar every year.”
at the start of the 4th paragraph.
This is not correct and the World Calendar is a counter-example, which adheres to the solar cycle just as well.
It is strict adherence to both the solar year and the
non-solar seven day week that produces an expiring calendar every year. The world calendar week may be regarded as a solar week, just like its months (or Gregorian months) can be regarded as solar months.
If one loosens the adherence to the solar year in the short term, then one can use the non-solar seven day week without the calendar expiring every year by means of a leap-week calendar.
It is possible that ‘solar cycle’ means the 28-year year cycle that the days of the week repeat in the Julian calendar and normally repeat in the Gregorian calendar, but I don’t think so, because the Gregorian Calendar does not strictly
adhere to this 28-year solar cycle. In this context, ‘solar’ refers to ‘Sunday’ and not ‘Solar’ as in Solar calendar (or Solar week). So I suggest not using ‘solar cycle’.
I’d suggest redrafting the sentence like:
“In contrast, the Gregorian Calendar's strict adherence to both the solar year and the seven-day week produces an expiring calendar