Ahmes and the MMP scribe explicitly used 256/81 for their value for pi. You use the term false addition, the proposed historical idea that others title false position. Peet and others had proposed the use of false position (and thereby, to my view, muddled the relatively easy to read vulgar fractions, as Ahmes used to solve all his algebra problems).
My view is that false position was an Arab innovation developed around 800 AD, 2,400 years too late to have been known by Ahmes and Egyptian scribes.
My proof is documented by all of Ahmes' algebra problems, RMP 24-38, 47, 80-81. Each of Ahmes' algebra problems had been solved in his shorthand by a small number of steps compared to the relatively awkward, and historically unproven Arab 'false position' method.
Robins-Shute's review of the RMP suggests that partial products and remainders were used (so Robins-Shute almost grasped the quotients and remainders used by Ahmes) to solve multiplication and division problems (page 18), a point missed by Peet and his group. Robins-Shute title for 'false position' was 'false supposition' (page 37), a term that discloses the odd modern revisionist nature of the method.
an answer than can not be directly found by 'false supposition'. Only the use of vulgar fractions as intermediate steps directly, and easily, solves this problem, a point that has been noted by several scholars.