1/2 - Bbar(p) = 4119*p**3/1372 - 344223*p**2/115934 - 526815*p/5200468 + 1/2
number of real roots of 1/2 - Bbar in [0,1]: 0 ; value at p=0: 1/2
number of real roots of 49788/100000 - Bbar in [0,1]: 0 ; value at p=0: 12447/25000
=> Bbar < 0.49788 on [0,1]  [CERTIFIED, exact]
max_[0,1] Bbar = 0.49787767885461794265 at p = 0.67596508573793118626  (exact critical point: 76494/232037 + sqrt(159156415444069)/36429809)
=> P[g=+1 | G_0=x] <= 0.4978776789 < 1/2 for all x, q:  s^L_E2 = 5/8  [CERTIFIED]
for reference: max Btilde (exact 1/pi) = 0.497854292771 at p = 0.675959539552
for reference: max of the sharper bound B = 0.490029476409 at p = 0.660163478611
x0 = 3.61976004892884,  I = 1.3588002107341e-5
s^U_E2 >= 5/8 + I       = 0.625013588002107
s_E2   >= 5/8 + (3/8) I = 0.62500509550079
