B  k = 4, n = 3: 256 f, 39 distinct H_f; cofactor > 0 on [q5-, q4+] fails for 0 (Arb) / 0 (Sturm); H == 0 identically for 0 f (expected the 2 ORs of 4 bits if n = k: True); g4 | H for 2 f (expected the 2 +-OR_S, |S| = 3: True); g5 | H for 0 f; (mult g4, mult g5) -> #f {(0, 0): 254, (1, 0): 2}; Delta(OR_S) formula for all S: True; float min of H_f over nonzero classes 4.441e-16 (0.0s)
B  k = 4, n = 4: 65536 f, 1630 distinct H_f; cofactor > 0 on [q5-, q4+] fails for 0 (Arb) / 0 (Sturm); H == 0 identically for 2 f (expected the 2 ORs of 4 bits if n = k: True); g4 | H for 8 f (expected the 8 +-OR_S, |S| = 3: True); g5 | H for 0 f; (mult g4, mult g5) -> #f {(0, 0): 65526, (1, 0): 8}; Delta(OR_S) formula for all S: True; float min of H_f over nonzero classes 4.441e-16 (1.3s)
B  k = 5, n = 3: 256 f, 39 distinct H_f; cofactor > 0 on [q6-, q5+] fails for 0 (Arb) / 0 (Sturm); H == 0 identically for 0 f (expected the 2 ORs of 5 bits if n = k: True); g5 | H for 0 f (expected the 0 +-OR_S, |S| = 4: True); g6 | H for 0 f; (mult g5, mult g6) -> #f {(0, 0): 256}; Delta(OR_S) formula for all S: True; float min of H_f over nonzero classes 5.120e-01 (0.0s)
B  k = 5, n = 4: 65536 f, 1630 distinct H_f; cofactor > 0 on [q6-, q5+] fails for 0 (Arb) / 0 (Sturm); H == 0 identically for 0 f (expected the 2 ORs of 5 bits if n = k: True); g5 | H for 2 f (expected the 2 +-OR_S, |S| = 4: True); g6 | H for 0 f; (mult g5, mult g6) -> #f {(0, 0): 65534, (1, 0): 2}; Delta(OR_S) formula for all S: True; float min of H_f over nonzero classes 0.000e+00 (1.8s)
X  Delta_i(f) by direct conditional expectation = polynomial table at q in {9/100, 1/10, 21/200}: 37704 comparisons, all equal
D  G_n(c) = tau max_f c . Delta(f) exactly, 48 random (u, c) with u in [u5, u6], n = 3, 4: all equal
S  G_n(c)^2 < T5^2 |c|^2 exactly (strict, as q < q5) at u in {2.911, 2.9107, 3, 3.1, 3.2, 3.236}: 2412 vectors, no violation; largest ratio of squares 0.999999039621 (at u = 2.9107 near u5, c = (1,1,1,1))
O  T4/T5 = -2*sqrt(5)/(5*q - 5) (increasing, = 1 only at q5), T6/T5 = sqrt(30)*(1 - q)/5 (decreasing, = 1 only at q6): True
O  (1,...,1)/sqrt(n) in the OR region (c_i > q sum c iff q < 1/n) for n = 5, 6 on [q6, q5]: True
O  OR-region identity exactly at 60 random (u, c), u in [u5, u6], n = 5, 6, c near (1,...,1): True
E  q5 + 0.0001: G_4(1,1,1,1)/(2 T5) = 1.0001118159; q6 - 0.0001: G_6(1,...,1)/(sqrt6 T5) = 1.00010954451; q5 + 1.0e-7: G_4(1,1,1,1)/(2 T5) = 1.0000001118; q6 - 1.0e-7: G_6(1,...,1)/(sqrt6 T5) = 1.00000010954
N  n = 3: on [q6, q5 + 1/1000] fails for 0 f; 20 -> 20 - 1e-6 fails for 0 f; k = 6 target 24 (1-q)^10 fails for 0 f; target 12 (1-q)^4 - 1e-6 fails for 2 f (the first three are expected to pass: 20 (1-q)^8 > 12 (1-q)^4 for q < 0.1199, 24 (1-q)^10 >= 12 (1-q)^4 for q <= 0.1091); informational: the stronger k = 4 bound 16 (1-q)^6 - sum Delta^2 > 0 on [q6-, q5+] fails for 0 f besides the 2 with H4 == 0 (n = 4 only)
N  n = 4: on [q6, q5 + 1/1000] fails for 2 f; 20 -> 20 - 1e-6 fails for 2 f; k = 6 target 24 (1-q)^10 fails for 32 f; informational: the stronger k = 4 bound 16 (1-q)^6 - sum Delta^2 > 0 on [q6-, q5+] fails for 0 f besides the 2 with H4 == 0 (n = 4 only)
A  q = 0.087129, n = 3: max G_n/T5 found 0.9295160031 at [0.5774 0.5774 0.5774]
A  q = 0.087129, n = 4: max G_n/T5 found 0.9797958971 at [0.5 0.5 0.5 0.5]
A  q = 0.087129, n = 5: max G_n/T5 found 1.0000000000 at [0.4472 0.4472 0.4472 0.4472 0.4472]
A  q = 0.087129, n = 6: max G_n/T5 found 1.0000000000 at [0.4472 0.4472 0.4472 0.4472 0.4472 0.    ]
A  q = 0.087129, n = 7: max G_n/T5 found 1.0000000000 at [ 0.4472  0.4472  0.4472  0.4472  0.4472 -0.     -0.    ]
A  q = 0.096351, n = 3: max G_n/T5 found 0.9485844975 at [0.5774 0.5774 0.5774]
A  q = 0.096351, n = 4: max G_n/T5 found 0.9897948557 at [0.5 0.5 0.5 0.5]
A  q = 0.096351, n = 5: max G_n/T5 found 1.0000000000 at [0.4472 0.4472 0.4472 0.4472 0.4472]
A  q = 0.096351, n = 6: max G_n/T5 found 1.0000000000 at [0.4472 0.4472 0.4472 0.4472 0.4472 0.    ]
A  q = 0.096351, n = 7: max G_n/T5 found 1.0000000000 at [0.4472 0.4472 0.4472 0.4472 0.4472 0.     0.    ]
A  q = 0.105573, n = 3: max G_n/T5 found 0.9682458366 at [0.5774 0.5774 0.5774]
A  q = 0.105573, n = 4: max G_n/T5 found 1.0000000000 at [0.5 0.5 0.5 0.5]
A  q = 0.105573, n = 5: max G_n/T5 found 1.0000000000 at [ 0.5  0.5  0.5  0.5 -0. ]
A  q = 0.105573, n = 6: max G_n/T5 found 1.0000000000 at [ 0.5  0.5  0.5  0.5 -0.  -0. ]
A  q = 0.105573, n = 7: max G_n/T5 found 1.0000000000 at [ 0.5  0.5  0.5  0.5  0.   0.  -0. ]
summary {'B4 (A.20 regression: 39 / 1630 classes)': True, 'B5': True, 'X': True, 'D': True, 'S': True, 'O': True, 'E': True, 'N': True, 'A (informational: MAIN-6 not claimed)': np.True_}
RESULT: ALL CHECKS PASSED (47s)

real	0m46.961s
user	0m48.052s
sys	0m0.232s
DONE-A22
