Hi Mark,

Mark Heaton wrote: We know that 9125 days is the number of days in 25 calendar years,

Almost Absolutely correct! 1 year = 12.3682662 lunar months...12.3682662 x 25 = 309.20665 if you are going to calculate it that way. It does not follow with Ancient Egyptian methods.
There are 12.3600646 lunar months in a solar year of 365 days. Actually the lunar year is 13 months of 29.53059 days for a total of 383.8977 days. The average length of a calendar month to be (10 * 384 - 1) / (10 * 13) = 29 69/130…29 69/130 x 13 = 3839/10 = 383.9 days in the lunar year.

Mark Heaton wrote: A circle with a radius of 250 royal cubits (diameter 500 royal cubits) has an equal area square with a side-length of:
365 x 34 digits, and a perimeter of 1,460 x 34 digits.

250^2 x 22/7 = diameter 500^2 / 14/11 = 196428 4/7 square cubits = circle area, the square root of 196428 4/7 = 443.2026302...443.2026302 x 28 = 12409.67365 digits...12409.67365 / 365 = 33.9991061 also 443.2026302 x 20.61 = 9134.406209 inches and the longest side socket length of G1 according to Petrie’s survey is 9130.8 for the East side noted here: <[www.ronaldbirdsall.com];

Mark Heaton wrote: There are, of course, precisely 309 lunar months in 25 calendar years of 365 days, or 9125 days.

Not exactly:
12.3682662 lunar months...12.3682662 x 25 years = 309.20665 x 34 = 10513.0261 days. Not 9125 days. 1460 / 25 = 58 4/10...58 4/10 x 10513.0261 = 613960.7242

Mark Heaton wrote: [/i]The number of lunar months in 500 calendar years is 6180[/i]

12.3682662 x 500 = 6184.1331 lunar months in 500 years not 6180 lunar months.

The synodic month, a.k.a. the mean lunar month, is the mean interval in days between conjunctions of the Moon and the Sun. The value of the synodic month is 29.53059 days. Thirteen synodic months is 383.8977 days, nearly 384 days.

Mark Heaton wrote: We know that 9125 days is the number of days in 25 calendar years, so we end up with a length of 34/25 digits symbolic of 1 day, and 1,460 x 34 digits symbolic of 100 calendar years of 365 days.

First: You have to demonstrate the Ancient Egyptians could divide the digit into 25 portions, all of the cubit rods demonstrate up to 16 divisions of the digit, for a maximum of 448 divisions of the cubit (28 x 16 = 448). Their system was Binary divisions by 2's.
Secondly:
1460 x 34 = 49640...49640 / 365 = 136 years
365 x 100 = 36500 / 34 = 1073 9/17
365 x 100 = 36500 / 25 = 1460
365 x 1461 / 1460 = 365 1/4 present solar year
365 x 1461 = 533265 days in one Sothic cycle
533265 / 29.5385 = 18053.05438 lunar months in one Sothic cycle.

Making the average length of a lunar month (10 * 384 - 1) / ( 10 * 13) = 29 69/130 or 29.53077 days, or 0.00018 days and would be out of sync with the lunar cycle by about one day every 450 years.

Mark Heaton wrote: My hypothesis, based on the evidence presented so far, was that the architect wanted to express the solar cycle in lunar months, and somehow had to integrate 309 lunar months in 25 calendar years and 1460 solar years in 1461 calendar years.

What cycle of the Sun or Moon would he be expressing with this number of lunar months?

Regards