S1 Lemma 3.5: 9841 words of length <= 8, kernels exactly over Q: dim ker M_s = [#U = #D]
S2 Lemma 3.7: enumeration N <= 12, k-sum and Vandermonde N <= 400, the bijection w -> (A, B) for N <= 7
S3 binomial series: (-4)^N binom(-1/2,N) = C(2N,N) (N <= 80); sum_(N<=200) C(2N,N) 8^-N <= sqrt 2 <= that + 2^-200, checked by squaring; sqrt(2)/4 = 0.3535533905932738
S4 Section 3.5: P(marker, U, D, I) = 1/2, 1/8, 1/8, 1/4; the cells E_(N,s,j) have total measure 1; with the exact kernel projections, sum_(s,j) mu(E_(N,s,j)) [(P)_(2j-1,2j-1) + (P)_(2j,2j)] = (1/4) C(2N,N) 8^-N for N <= 7
S5 Remark 3.8: coefficients of x^2 (1-4x^4)^(-1/2) up to x^63: C(2N,N) at x^(4N+2), zero elsewhere
   K=3: d_K = 5/4 = 1.25000000, d_K - sqrt(2)/4 = 8.96e-01  [printed: 1.2500000, 9.0e-01]
   K=6: d_K = 33/64 = 0.51562500, d_K - sqrt(2)/4 = 1.62e-01  [printed: 0.5156250, 1.6e-01]
   K=9: d_K = 101/256 = 0.39453125, d_K - sqrt(2)/4 = 4.10e-02  [printed: 0.3945313, 4.1e-02]
   K=12: d_K = 2993/8192 = 0.36535645, d_K - sqrt(2)/4 = 1.18e-02  [printed: 0.3653564, 1.2e-02]
   K=15: d_K = 29263/81920 = 0.35721436, d_K - sqrt(2)/4 = 3.66e-03  [printed: 0.3572144, 3.7e-03]
   K=18: d_K = 92995/262144 = 0.35474777, d_K - sqrt(2)/4 = 1.19e-03  [printed: 0.3547478, 1.2e-03]
   K=21: d_K = 2598067/7340032 = 0.35395854, d_K - sqrt(2)/4 = 4.05e-04  [printed: 0.3539585, 4.1e-04]
   K=30: d_K = (not printed as a fraction) = 0.35357242, d_K - sqrt(2)/4 = 1.90e-05  [printed: 0.3535724, 1.9e-05]
   K=60: d_K = (not printed as a fraction) = 0.35355339, d_K - sqrt(2)/4 = 3.17e-09  [printed: 0.3535534, 3.2e-09]
S6 Table 1 as printed (fractions, 7 decimals, differences to two digits); Remark 4.3: the identity for P <= 120 (exact) and the bound |d_3P - sqrt(2)/4| <= 2^-(P+1) + 2(3/8)^P/P for P <= 120
S7 Section 5: (sqrt 2/4)^2 = 1/8; the squares of (1/8) sqrt(2^t/(2^t-1)), 3 <= t <= 200, lie in (1/64, 1/56]; t = 3 is (1/4) sqrt(2/7)
S8 line: 1500 random windows of 180 indices: 531000 rows equal to 8 x those of Lemma 3.3 (three classes), 128246 segment blocks equal to 8 M_s and met by no other row of the window
checks: 560429, failures: 0
ALL CHECKS PASSED
time 26.8 s
