h = ('-5/8', '1/8', '1/8', '-1/8'): mu = -1/8, b = -1/4, eps = +1, lambda_+ = -5/16, lambda_- = 17/80
  nu* = +1, a = 5/16, lambda' = 17/80, a2 = 125/4096, M' = 17/256, q = 3/7, beta = 1/3
  (M' - a q)/(1 - q) = -121/1024; admissible A in [125/4096, 5/16); using A = 17/256
  sigma h(2p-1, 2p-1) = 1/8 + (-1/2) p + (1) p^2
  on [0, 3/7]: Phi+ = 1/8 + (-43/64) p + (63/64) p^2, discriminant -167/4096, min = 167/16128 (~1.0355e-02)
  on [3/7, 4/7]: Phi+ = 1/8 + (-13/16) p + (21/16) p^2, discriminant 1/256, min = 1/56 (~1.7857e-02)
  on [4/7, 1]: Phi+ = -1/16 + (-19/64) p + (63/64) p^2, discriminant 1369/4096, min = 5/56 (~8.9286e-02)
  Phi+ >= 0 on [0,1]: True
h = ('-3/4', '1/8', '1/8', '-1/8'): mu = -5/32, b = -9/32, eps = +1, lambda_+ = -67/176, lambda_- = 11/48
  nu* = +1, a = 67/176, lambda' = 11/48, a2 = 300763/5451776, M' = 67/768, q = 11/27, beta = 5/11
  (M' - a q)/(1 - q) = -469/4096; admissible A in [300763/5451776, 67/176); using A = 300763/5451776
  sigma h(2p-1, 2p-1) = 1/8 + (-1/2) p + (9/8) p^2
  on [0, 11/27]: Phi+ = 1/8 + (-1938809/2725888) p + (30602691/29984768) p^2, discriminant -32815487183/7430465388544, min = 32815487183/30334366605312 (~1.0818e-03)
  on [11/27, 16/27]: Phi+ = 1/8 + (-1307/1408) p + (2187/1408) p^2, discriminant 168601/1982464, min = 1/216 (~4.6296e-03)
  on [16/27, 1]: Phi+ = -357287/1874048 + (-2397523/29984768) p + (30602691/29984768) p^2, discriminant 5830748022577/7430465388544, min = 13/108 (~1.2037e-01)
  Phi+ >= 0 on [0,1]: True
comparison, A = max(a2, M') (the coefficient of the first version):
h = ('-3/4', '1/8', '1/8', '-1/8'): mu = -5/32, b = -9/32, eps = +1, lambda_+ = -67/176, lambda_- = 11/48
  nu* = +1, a = 67/176, lambda' = 11/48, a2 = 300763/5451776, M' = 67/768, q = 11/27, beta = 5/11
  (M' - a q)/(1 - q) = -469/4096; admissible A in [300763/5451776, 67/176); using A = 67/768
  sigma h(2p-1, 2p-1) = 1/8 + (-1/2) p + (9/8) p^2
  on [0, 11/27]: Phi+ = 1/8 + (-211/288) p + (4155/3872) p^2, discriminant 2161/10036224, min = -2161/43079040 (~-5.0164e-05)
  on [11/27, 16/27]: Phi+ = 1/8 + (-1307/1408) p + (2187/1408) p^2, discriminant 168601/1982464, min = 1/216 (~4.6296e-03)
  on [16/27, 1]: Phi+ = -695/4356 + (-5699/34848) p + (4155/3872) p^2, discriminant 7141681/10036224, min = 13/108 (~1.2037e-01)
  Phi+ >= 0 on [0,1]: False

Paragraph 'Examples' after Corollary 10.8: exact assertions
m = 6, h = (-5/8, 1/8, 1/8, -1/8): Theorem F: Phi(t,t) = 3/64 + t/4 + (21/64) t^2, min = -1/1344 at t = -8/21 < 0
  dictator decoder (k = 1, nu = +1, F(z) = z): Gamma = -1/56, E F = -1/7 = 2q - 1
  A = M' = 17/256: 256 Phi+ = 32 - 172p + 252p^2 on [0,3/7] (disc -2672), 16 Phi+ = 2 - 13p + 21p^2 = (7p-2)(3p-1) on [3/7,4/7], 64 Phi+ = -4 - 19p + 63p^2 on [4/7,1] (increasing, 40/7 at 4/7)
  min Phi+ = 167/16128 at p = 43/126; Phi+(3/7) = 1/56 = -Gamma(dictator)  [EXACT]
m = 7, h = (-3/4, 1/8, 1/8, -1/8): A = a^3 = 300763/5451776 admissible; min Phi+ = 32815487183/30334366605312 (~1.08e-03), 1/216 (at p = 11/27), 13/108
  dictator decoder (k = 1, nu = +1, F(z) = z): sigma Gamma = 1/216 = Phi+(11/27), E F = -5/27
  A = M' = 67/768: min on [0, 11/27] = -2161/43079040 < 0
  Theorem F: Phi(t,t) = 277/5632 + 5/16 t + 2187/5632 t^2, min = -168601/12317184 ~ -0.013688 at t = -880/2187  [EXACT]
mirror images h(-w): same data, same minima on the reflected intervals, Phi+_mirror(p) = Phi+(1-p); B(p) and the
  three pieces agree with the definition on p = j/378; Phi+ - Phi(2p-1,2p-1) = 4|b|[(rho-a)p(1-p) + (a-A)(p(1-p)-B)] >= 0  [EXACT]
m = 6: 1366 decoders ({-1,0,1}-valued, k <= 2; {-1,1}-valued, k = 3): sigma Gamma >= Phi+(p) >= Phi(2p-1,2p-1) for each; min sigma Gamma = 1/56 (nu = (1,), F = (1, -1)); dictator 1/56  [EXACT]
m = 7: 1366 decoders ({-1,0,1}-valued, k <= 2; {-1,1}-valued, k = 3): sigma Gamma >= Phi+(p) >= Phi(2p-1,2p-1) for each; min sigma Gamma = 1/216 (nu = (1,), F = (1, -1)); dictator 1/216  [EXACT]
All numbers of the paragraph 'Examples' (Section 10) verified exactly.
