PFR bookkeeping: where GGMT's 2K^12 comes from (three easy-to-lose factors)

When formalizing Marton/PFR in F_2^n from the entropic version, three places silently cost exponent. (1) Second estimate: fibre (X1, X1~) against (X2, X2~), not X1 against X1~; then both minimality comparisons cost d_ii/2 because I[X1 : X1+X1~] = H[X1+X1~] - H[X1] = d(X1,X1) in char 2, giving I2 <= eta(d11+d22) and an endgame k <= (8 eta + eta^2) k, so eta = 1/9 works. The other pairing only gives I2 <= d11+d22-2(1-eta)k and forces eta < 1/15. (2) For sets use p1 = p2 = U_A: tau(U_A,U_A) = (1+2 eta) d0, so d(U_A,U_H) <= (1/eta+2)/2 log K = 11/2 log K, versus 13 in general. (3) In the covering step keep the square: |c||A'| <= K|A| and |A||H| <= K^C |A'|^2 give |c|^2 |H| <= K^{C+2}|A|; bounding |A| <= K^C|A'| first loses K^C. If |H| > |A|, shrink to H' <= H with |H'| <= |A| < 2|H'| and cover H by translates of H' (Ruzsa covering again). Total: < 2K^{C+1} = 2K^12.