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This has turned out to be a very simple calculation.
If the GP base is 1777.777r units x 20.625 = 36666.666r imperial inches the the ancient inch comes into play as 100/39.375
100/39.375 = 2.53968254 x 7 = 17.777r exactly x 17.777r = 316.0493827 100 Egyptian pis.
So the GP is designed against this ancient unit of measure if 36666.666r can be accepted.