The issue of theoretical geometry is posed. I would also like to add the issue of theoretical arithmetic. My view is that theoretical arithmetic is present in Middle Kingdom texts, beginning with the Akhmim Wooden Tablet, and its use of a hekat defined as 64/64, and exactly partitioned into quotients and scaled remainders.
I can not answer the theoretical geometry question, the mathematical question that is posed when 'sacred' geometry is introduced.
My view is that, prior to the building of the pyramids, and the obvious theoretical and practical geometric construction issues, the "Book of the Dead" tradition focuses on the balance beam, first operated by binary weights to weigh the heart. At the beginning of the Old Kingdom, binary weights could not have exactly weighed every heart.
To solve the Horus-Eye number aspect of balance beam weights, any possible weight must be available, much as the Akhmim Wooden Tablet scribe went beyond binary quotients to find any needed Egyptian fraction remainder, scaled to ro, 1/320 of a hekat.
Returning to the theoretical geometry issue, I know of no Old Kingdom or Middle Kingdom text that clearly sets out statements, calculations, and proofs that are equivalent to the arithmetic statements, calculations and proofs presented in the five Akhmim Wooden Tablet division of a hekat problems.
ps: When I find the location of Sylvia Couchard's MMP treatise, I'll post it here.