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Notes -
You're right; just keep it a solar calendar, and let the moon precess as much as it wants.
New Year's Day would actually be a bonus for programmers: the zeroth day of the new year, and the first and only day in the zeroth month, keeping all the Saturdays divisible by seven.
Since you've dropped the lunar aspects, you can just intercalate a whole week at a time instead of having an orphan day every year, although this would cause the equinoxes and solstices to drift.
https://en.wikipedia.org/wiki/Pax_Calendar
Your proposal seems to be: https://en.wikipedia.org/wiki/International_Fixed_Calendar
I independently derived it, and chose a different location and name for the new month, but it’s fundamentally identical to the IFC, yes. I chose the name Leftober because it’s made from the leftover 2 or 3 days from the other months. Also, from the article:
13 is my favorite prime number and 91 my favorite nonprime. It’s 7x13, a semiprime, and the only composite below 100 which can’t be factored by tricks and must be memorized:
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