How can we be sure that the equinox was on the 21 if the calendar Is off?

AI Overview - Still on December 21st
13-month calendar system, the Winter Solstice is strategically placed, often as Day 0 or the first day of the year (Year 1, Month 1, Day 1), usually falling on December 21st, marking the start of the year and the shortest day, with leap days added at year-end, keeping the solstice consistent and aligning with the Gregorian calendar's cycle for simplicity and cultural significance.
An extra day (or two in leap years) is added at the end of the year, often as "Day 0" or "Year-End Day," which coincides with the Winter Solstice (around Dec 21st) in the Northern Hemisphere.
This system ensures the solstice always falls on the same date (e.g., Dec 21st) or very close to it, unlike the Gregorian calendar where it shifts slightly.
Example (Calendar 13):
Year Start: December 21st (Solstice Day).
Months: 13 months, each with 28 days, followed by the year-end day.