CLASS-I CUBATURE f=23,f=24 EXACT VERIFICATION LEDGER v1.1
All arithmetic for equality/sign decisions is exact in Q(sqrt(5)); decimals are metadata only.

FREQUENCY 23
target_degree=71
nodes=5292
orbits=56
moment_rows=52
rank=52
affine_dimension=4

ORBIT ORDER:
00 (23, 0, 0)
01 (22, 1, 0)
02 (21, 2, 0)
03 (21, 1, 1)
04 (20, 3, 0)
05 (20, 2, 1)
06 (19, 4, 0)
07 (19, 3, 1)
08 (19, 2, 2)
09 (18, 5, 0)
10 (18, 4, 1)
11 (18, 3, 2)
12 (17, 6, 0)
13 (17, 5, 1)
14 (17, 4, 2)
15 (17, 3, 3)
16 (16, 7, 0)
17 (16, 6, 1)
18 (16, 5, 2)
19 (16, 4, 3)
20 (15, 8, 0)
21 (15, 7, 1)
22 (15, 6, 2)
23 (15, 5, 3)
24 (15, 4, 4)
25 (14, 9, 0)
26 (14, 8, 1)
27 (14, 7, 2)
28 (14, 6, 3)
29 (14, 5, 4)
30 (13, 10, 0)
31 (13, 9, 1)
32 (13, 8, 2)
33 (13, 7, 3)
34 (13, 6, 4)
35 (13, 5, 5)
36 (12, 11, 0)
37 (12, 10, 1)
38 (12, 9, 2)
39 (12, 8, 3)
40 (12, 7, 4)
41 (12, 6, 5)
42 (11, 11, 1)
43 (11, 10, 2)
44 (11, 9, 3)
45 (11, 8, 4)
46 (11, 7, 5)
47 (11, 6, 6)
48 (10, 10, 3)
49 (10, 9, 4)
50 (10, 8, 5)
51 (10, 7, 6)
52 (9, 9, 5)
53 (9, 8, 6)
54 (9, 7, 7)
55 (8, 8, 7)

EXACT WEIGHT SIGN CHECKS:
00 (23, 0, 0) sign=+1
01 (22, 1, 0) sign=+1
02 (21, 2, 0) sign=+1
03 (21, 1, 1) sign=+1
04 (20, 3, 0) sign=+1
05 (20, 2, 1) sign=+1
06 (19, 4, 0) sign=+1
07 (19, 3, 1) sign=+1
08 (19, 2, 2) sign=+1
09 (18, 5, 0) sign=+1
10 (18, 4, 1) sign=+1
11 (18, 3, 2) sign=+1
12 (17, 6, 0) sign=+1
13 (17, 5, 1) sign=+1
14 (17, 4, 2) sign=+1
15 (17, 3, 3) sign=+1
16 (16, 7, 0) sign=+1
17 (16, 6, 1) sign=+1
18 (16, 5, 2) sign=+1
19 (16, 4, 3) sign=+1
20 (15, 8, 0) sign=+1
21 (15, 7, 1) sign=+1
22 (15, 6, 2) sign=+1
23 (15, 5, 3) sign=+1
24 (15, 4, 4) sign=+1
25 (14, 9, 0) sign=+1
26 (14, 8, 1) sign=+1
27 (14, 7, 2) sign=+1
28 (14, 6, 3) sign=+1
29 (14, 5, 4) sign=+1
30 (13, 10, 0) sign=+1
31 (13, 9, 1) sign=+1
32 (13, 8, 2) sign=+1
33 (13, 7, 3) sign=+1
34 (13, 6, 4) sign=+1
35 (13, 5, 5) sign=+1
36 (12, 11, 0) sign=+1
37 (12, 10, 1) sign=+1
38 (12, 9, 2) sign=+1
39 (12, 8, 3) sign=+1
40 (12, 7, 4) sign=+1
41 (12, 6, 5) sign=+1
42 (11, 11, 1) sign=+1
43 (11, 10, 2) sign=+1
44 (11, 9, 3) sign=+1
45 (11, 8, 4) sign=+1
46 (11, 7, 5) sign=+1
47 (11, 6, 6) sign=+1
48 (10, 10, 3) sign=+1
49 (10, 9, 4) sign=+1
50 (10, 8, 5) sign=+1
51 (10, 7, 6) sign=+1
52 (9, 9, 5) sign=+1
53 (9, 8, 6) sign=+1
54 (9, 7, 7) sign=+1
55 (8, 8, 7) sign=+1

EXACT SUM: a=1 b=0 (must be 1,0)

EXACT MOMENT RESIDUALS:
00 degree=00 (r,s)=(0, 0) residual_a=0 residual_b=0
01 degree=06 (r,s)=(1, 0) residual_a=0 residual_b=0
02 degree=10 (r,s)=(0, 1) residual_a=0 residual_b=0
03 degree=12 (r,s)=(2, 0) residual_a=0 residual_b=0
04 degree=16 (r,s)=(1, 1) residual_a=0 residual_b=0
05 degree=18 (r,s)=(3, 0) residual_a=0 residual_b=0
06 degree=20 (r,s)=(0, 2) residual_a=0 residual_b=0
07 degree=22 (r,s)=(2, 1) residual_a=0 residual_b=0
08 degree=24 (r,s)=(4, 0) residual_a=0 residual_b=0
09 degree=26 (r,s)=(1, 2) residual_a=0 residual_b=0
10 degree=28 (r,s)=(3, 1) residual_a=0 residual_b=0
11 degree=30 (r,s)=(5, 0) residual_a=0 residual_b=0
12 degree=30 (r,s)=(0, 3) residual_a=0 residual_b=0
13 degree=32 (r,s)=(2, 2) residual_a=0 residual_b=0
14 degree=34 (r,s)=(4, 1) residual_a=0 residual_b=0
15 degree=36 (r,s)=(6, 0) residual_a=0 residual_b=0
16 degree=36 (r,s)=(1, 3) residual_a=0 residual_b=0
17 degree=38 (r,s)=(3, 2) residual_a=0 residual_b=0
18 degree=40 (r,s)=(5, 1) residual_a=0 residual_b=0
19 degree=40 (r,s)=(0, 4) residual_a=0 residual_b=0
20 degree=42 (r,s)=(7, 0) residual_a=0 residual_b=0
21 degree=42 (r,s)=(2, 3) residual_a=0 residual_b=0
22 degree=44 (r,s)=(4, 2) residual_a=0 residual_b=0
23 degree=46 (r,s)=(6, 1) residual_a=0 residual_b=0
24 degree=46 (r,s)=(1, 4) residual_a=0 residual_b=0
25 degree=48 (r,s)=(8, 0) residual_a=0 residual_b=0
26 degree=48 (r,s)=(3, 3) residual_a=0 residual_b=0
27 degree=50 (r,s)=(5, 2) residual_a=0 residual_b=0
28 degree=50 (r,s)=(0, 5) residual_a=0 residual_b=0
29 degree=52 (r,s)=(7, 1) residual_a=0 residual_b=0
30 degree=52 (r,s)=(2, 4) residual_a=0 residual_b=0
31 degree=54 (r,s)=(9, 0) residual_a=0 residual_b=0
32 degree=54 (r,s)=(4, 3) residual_a=0 residual_b=0
33 degree=56 (r,s)=(6, 2) residual_a=0 residual_b=0
34 degree=56 (r,s)=(1, 5) residual_a=0 residual_b=0
35 degree=58 (r,s)=(8, 1) residual_a=0 residual_b=0
36 degree=58 (r,s)=(3, 4) residual_a=0 residual_b=0
37 degree=60 (r,s)=(10, 0) residual_a=0 residual_b=0
38 degree=60 (r,s)=(5, 3) residual_a=0 residual_b=0
39 degree=60 (r,s)=(0, 6) residual_a=0 residual_b=0
40 degree=62 (r,s)=(7, 2) residual_a=0 residual_b=0
41 degree=62 (r,s)=(2, 5) residual_a=0 residual_b=0
42 degree=64 (r,s)=(9, 1) residual_a=0 residual_b=0
43 degree=64 (r,s)=(4, 4) residual_a=0 residual_b=0
44 degree=66 (r,s)=(11, 0) residual_a=0 residual_b=0
45 degree=66 (r,s)=(6, 3) residual_a=0 residual_b=0
46 degree=66 (r,s)=(1, 6) residual_a=0 residual_b=0
47 degree=68 (r,s)=(8, 2) residual_a=0 residual_b=0
48 degree=68 (r,s)=(3, 5) residual_a=0 residual_b=0
49 degree=70 (r,s)=(10, 1) residual_a=0 residual_b=0
50 degree=70 (r,s)=(5, 4) residual_a=0 residual_b=0
51 degree=70 (r,s)=(0, 7) residual_a=0 residual_b=0

RANK WITNESS modulus=1000000000000000031
det(+sqrt5) mod p=650097745717062046
det(-sqrt5) mod p=139778200766197651

EXACT MINIMUM ORBIT=(21, 1, 1)
minimum_decimal_60=0.003777725693780652542084082262449790124026578124021415259901

FREQUENCY 24
target_degree=75
nodes=5762
orbits=61
moment_rows=57
rank=57
affine_dimension=4

ORBIT ORDER:
00 (24, 0, 0)
01 (23, 1, 0)
02 (22, 2, 0)
03 (22, 1, 1)
04 (21, 3, 0)
05 (21, 2, 1)
06 (20, 4, 0)
07 (20, 3, 1)
08 (20, 2, 2)
09 (19, 5, 0)
10 (19, 4, 1)
11 (19, 3, 2)
12 (18, 6, 0)
13 (18, 5, 1)
14 (18, 4, 2)
15 (18, 3, 3)
16 (17, 7, 0)
17 (17, 6, 1)
18 (17, 5, 2)
19 (17, 4, 3)
20 (16, 8, 0)
21 (16, 7, 1)
22 (16, 6, 2)
23 (16, 5, 3)
24 (16, 4, 4)
25 (15, 9, 0)
26 (15, 8, 1)
27 (15, 7, 2)
28 (15, 6, 3)
29 (15, 5, 4)
30 (14, 10, 0)
31 (14, 9, 1)
32 (14, 8, 2)
33 (14, 7, 3)
34 (14, 6, 4)
35 (14, 5, 5)
36 (13, 11, 0)
37 (13, 10, 1)
38 (13, 9, 2)
39 (13, 8, 3)
40 (13, 7, 4)
41 (13, 6, 5)
42 (12, 12, 0)
43 (12, 11, 1)
44 (12, 10, 2)
45 (12, 9, 3)
46 (12, 8, 4)
47 (12, 7, 5)
48 (12, 6, 6)
49 (11, 11, 2)
50 (11, 10, 3)
51 (11, 9, 4)
52 (11, 8, 5)
53 (11, 7, 6)
54 (10, 10, 4)
55 (10, 9, 5)
56 (10, 8, 6)
57 (10, 7, 7)
58 (9, 9, 6)
59 (9, 8, 7)
60 (8, 8, 8)

EXACT WEIGHT SIGN CHECKS:
00 (24, 0, 0) sign=+1
01 (23, 1, 0) sign=+1
02 (22, 2, 0) sign=+1
03 (22, 1, 1) sign=+1
04 (21, 3, 0) sign=+1
05 (21, 2, 1) sign=+1
06 (20, 4, 0) sign=+1
07 (20, 3, 1) sign=+1
08 (20, 2, 2) sign=+1
09 (19, 5, 0) sign=+1
10 (19, 4, 1) sign=+1
11 (19, 3, 2) sign=+1
12 (18, 6, 0) sign=+1
13 (18, 5, 1) sign=+1
14 (18, 4, 2) sign=+1
15 (18, 3, 3) sign=+1
16 (17, 7, 0) sign=+1
17 (17, 6, 1) sign=+1
18 (17, 5, 2) sign=+1
19 (17, 4, 3) sign=+1
20 (16, 8, 0) sign=+1
21 (16, 7, 1) sign=+1
22 (16, 6, 2) sign=+1
23 (16, 5, 3) sign=+1
24 (16, 4, 4) sign=+1
25 (15, 9, 0) sign=+1
26 (15, 8, 1) sign=+1
27 (15, 7, 2) sign=+1
28 (15, 6, 3) sign=+1
29 (15, 5, 4) sign=+1
30 (14, 10, 0) sign=+1
31 (14, 9, 1) sign=+1
32 (14, 8, 2) sign=+1
33 (14, 7, 3) sign=+1
34 (14, 6, 4) sign=+1
35 (14, 5, 5) sign=+1
36 (13, 11, 0) sign=+1
37 (13, 10, 1) sign=+1
38 (13, 9, 2) sign=+1
39 (13, 8, 3) sign=+1
40 (13, 7, 4) sign=+1
41 (13, 6, 5) sign=+1
42 (12, 12, 0) sign=+1
43 (12, 11, 1) sign=+1
44 (12, 10, 2) sign=+1
45 (12, 9, 3) sign=+1
46 (12, 8, 4) sign=+1
47 (12, 7, 5) sign=+1
48 (12, 6, 6) sign=+1
49 (11, 11, 2) sign=+1
50 (11, 10, 3) sign=+1
51 (11, 9, 4) sign=+1
52 (11, 8, 5) sign=+1
53 (11, 7, 6) sign=+1
54 (10, 10, 4) sign=+1
55 (10, 9, 5) sign=+1
56 (10, 8, 6) sign=+1
57 (10, 7, 7) sign=+1
58 (9, 9, 6) sign=+1
59 (9, 8, 7) sign=+1
60 (8, 8, 8) sign=+1

EXACT SUM: a=1 b=0 (must be 1,0)

EXACT MOMENT RESIDUALS:
00 degree=00 (r,s)=(0, 0) residual_a=0 residual_b=0
01 degree=06 (r,s)=(1, 0) residual_a=0 residual_b=0
02 degree=10 (r,s)=(0, 1) residual_a=0 residual_b=0
03 degree=12 (r,s)=(2, 0) residual_a=0 residual_b=0
04 degree=16 (r,s)=(1, 1) residual_a=0 residual_b=0
05 degree=18 (r,s)=(3, 0) residual_a=0 residual_b=0
06 degree=20 (r,s)=(0, 2) residual_a=0 residual_b=0
07 degree=22 (r,s)=(2, 1) residual_a=0 residual_b=0
08 degree=24 (r,s)=(4, 0) residual_a=0 residual_b=0
09 degree=26 (r,s)=(1, 2) residual_a=0 residual_b=0
10 degree=28 (r,s)=(3, 1) residual_a=0 residual_b=0
11 degree=30 (r,s)=(5, 0) residual_a=0 residual_b=0
12 degree=30 (r,s)=(0, 3) residual_a=0 residual_b=0
13 degree=32 (r,s)=(2, 2) residual_a=0 residual_b=0
14 degree=34 (r,s)=(4, 1) residual_a=0 residual_b=0
15 degree=36 (r,s)=(6, 0) residual_a=0 residual_b=0
16 degree=36 (r,s)=(1, 3) residual_a=0 residual_b=0
17 degree=38 (r,s)=(3, 2) residual_a=0 residual_b=0
18 degree=40 (r,s)=(5, 1) residual_a=0 residual_b=0
19 degree=40 (r,s)=(0, 4) residual_a=0 residual_b=0
20 degree=42 (r,s)=(7, 0) residual_a=0 residual_b=0
21 degree=42 (r,s)=(2, 3) residual_a=0 residual_b=0
22 degree=44 (r,s)=(4, 2) residual_a=0 residual_b=0
23 degree=46 (r,s)=(6, 1) residual_a=0 residual_b=0
24 degree=46 (r,s)=(1, 4) residual_a=0 residual_b=0
25 degree=48 (r,s)=(8, 0) residual_a=0 residual_b=0
26 degree=48 (r,s)=(3, 3) residual_a=0 residual_b=0
27 degree=50 (r,s)=(5, 2) residual_a=0 residual_b=0
28 degree=50 (r,s)=(0, 5) residual_a=0 residual_b=0
29 degree=52 (r,s)=(7, 1) residual_a=0 residual_b=0
30 degree=52 (r,s)=(2, 4) residual_a=0 residual_b=0
31 degree=54 (r,s)=(9, 0) residual_a=0 residual_b=0
32 degree=54 (r,s)=(4, 3) residual_a=0 residual_b=0
33 degree=56 (r,s)=(6, 2) residual_a=0 residual_b=0
34 degree=56 (r,s)=(1, 5) residual_a=0 residual_b=0
35 degree=58 (r,s)=(8, 1) residual_a=0 residual_b=0
36 degree=58 (r,s)=(3, 4) residual_a=0 residual_b=0
37 degree=60 (r,s)=(10, 0) residual_a=0 residual_b=0
38 degree=60 (r,s)=(5, 3) residual_a=0 residual_b=0
39 degree=60 (r,s)=(0, 6) residual_a=0 residual_b=0
40 degree=62 (r,s)=(7, 2) residual_a=0 residual_b=0
41 degree=62 (r,s)=(2, 5) residual_a=0 residual_b=0
42 degree=64 (r,s)=(9, 1) residual_a=0 residual_b=0
43 degree=64 (r,s)=(4, 4) residual_a=0 residual_b=0
44 degree=66 (r,s)=(11, 0) residual_a=0 residual_b=0
45 degree=66 (r,s)=(6, 3) residual_a=0 residual_b=0
46 degree=66 (r,s)=(1, 6) residual_a=0 residual_b=0
47 degree=68 (r,s)=(8, 2) residual_a=0 residual_b=0
48 degree=68 (r,s)=(3, 5) residual_a=0 residual_b=0
49 degree=70 (r,s)=(10, 1) residual_a=0 residual_b=0
50 degree=70 (r,s)=(5, 4) residual_a=0 residual_b=0
51 degree=70 (r,s)=(0, 7) residual_a=0 residual_b=0
52 degree=72 (r,s)=(12, 0) residual_a=0 residual_b=0
53 degree=72 (r,s)=(7, 3) residual_a=0 residual_b=0
54 degree=72 (r,s)=(2, 6) residual_a=0 residual_b=0
55 degree=74 (r,s)=(9, 2) residual_a=0 residual_b=0
56 degree=74 (r,s)=(4, 5) residual_a=0 residual_b=0

RANK WITNESS modulus=1000000000000000031
det(+sqrt5) mod p=550949013298233594
det(-sqrt5) mod p=966277299582556251

EXACT MINIMUM ORBIT=(23, 1, 0)
minimum_decimal_60=0.003412253320984930573099634686301743266126075350598455734277

