(1) Boolean equality cases of the second inequality (exact):
  n=1 q=1/5: all 4 Boolean f satisfy the bound; equality for exactly the 2 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=1 q=3/10: all 4 Boolean f satisfy the bound; equality for exactly the 2 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=1 q=1/3: all 4 Boolean f satisfy the bound; equality for exactly the 2 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=1 q=2/5: all 4 Boolean f satisfy the bound; equality for exactly the 2 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=2 q=1/5: all 16 Boolean f satisfy the bound; equality for exactly the 6 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=2 q=3/10: all 16 Boolean f satisfy the bound; equality for exactly the 6 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=2 q=1/3: all 16 Boolean f satisfy the bound; equality for exactly the 6 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=2 q=2/5: all 16 Boolean f satisfy the bound; equality for exactly the 6 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=3 q=1/5: all 256 Boolean f satisfy the bound; equality for exactly the 13 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=3 q=3/10: all 256 Boolean f satisfy the bound; equality for exactly the 13 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=3 q=1/3: all 256 Boolean f satisfy the bound; equality for exactly the 13 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=3 q=2/5: all 256 Boolean f satisfy the bound; equality for exactly the 13 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=4 q=1/5: all 65536 Boolean f satisfy the bound; equality for exactly the 23 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=4 q=3/10: all 65536 Boolean f satisfy the bound; equality for exactly the 23 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=4 q=1/3: all 65536 Boolean f satisfy the bound; equality for exactly the 23 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
  n=4 q=2/5: all 65536 Boolean f satisfy the bound; equality for exactly the 23 listed ones (0, 1{x_i=1}, 1{x_i=x_j=1}, 1{x_i=1,x_j=-1})
(2) equality cases of the first inequality among nonnegative f of degree <= 2 (exact):
  1422 equality cases and 1564 strict cases among random nonnegative degree<=2 f on {-1,1}^4; equality <=> intersecting support <=> listed form; (E f)^2/E f^2 in [q^2, q] for all equality cases (ranges found: q=1/5: [0.0400, 0.1970], q=3/10: [0.0900, 0.2955], q=1/3: [0.1111, 0.3256], q=2/5: [0.1600, 0.3919])
(3) ANDs of t coordinates (exact):
  q=1/5: W^1(AND_t)/(qp+beta p^2), t=1..8: 1.0000 1.0000 0.4286 0.1250 0.0318 0.0077 0.0018 0.0004
  q=3/10: W^1(AND_t)/(qp+beta p^2), t=1..8: 1.0000 1.0000 0.5625 0.2432 0.0935 0.0339 0.0119 0.0041
  q=1/3: W^1(AND_t)/(qp+beta p^2), t=1..8: 1.0000 1.0000 0.6000 0.2857 0.1220 0.0492 0.0192 0.0073
  q=2/5: W^1(AND_t)/(qp+beta p^2), t=1..8: 1.0000 1.0000 0.6667 0.3721 0.1896 0.0917 0.0429 0.0196
  q=1/2: W^1(AND_t)/(qp+beta p^2), t=1..8: 1.0000 1.0000 0.7500 0.5000 0.3125 0.1875 0.1094 0.0625
(4) small means (floating point):
  small-mean bound holds on all tested f (largest ratio W^1/bound = 0.7504)
  q=0.3: AND_t constant (1-q)/(q ln(1/q)) = 1.9380 <= 1/(2q(1-q)) = 2.3810
  q=0.4: AND_t constant (1-q)/(q ln(1/q)) = 1.6370 <= 1/(2q(1-q)) = 2.0833
  q=0.5: AND_t constant (1-q)/(q ln(1/q)) = 1.4427 <= 1/(2q(1-q)) = 2.0000
