{
  "description": "Doche limit-point construction with jointly optimized denominator multiplicities and rational numerator weights; numerator factors discovered by dual-measure integer evaluation lattices and LLL. Verification is recorded separately.",
  "target": "0.2534449",
  "grid": 524288,
  "numeric_unverified": 0.2534446872174579,
  "denominator": [
    {
      "name": "Q1",
      "coeffs": [
        1,
        -7,
        30,
        -97,
        269,
        -679,
        1612,
        -3618,
        7646,
        -15180,
        28457,
        -50741,
        86189,
        -138288,
        206152,
        -279897,
        339335,
        -360911,
        331775,
        -260367,
        172556,
        -95554,
        43677,
        -16221,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "multiplicity": 18594304
    },
    {
      "name": "Q2",
      "coeffs": [
        1,
        -7,
        30,
        -96,
        255,
        -586,
        1212,
        -2360,
        4573,
        -9148,
        18749,
        -37783,
        71770,
        -124910,
        195848,
        -273368,
        335981,
        -359545,
        331349,
        -260271,
        172542,
        -95553,
        43677,
        -16221,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "multiplicity": 5575669
    },
    {
      "name": "R0",
      "coeffs": [
        1,
        -7,
        31,
        -107,
        321,
        -867,
        2148,
        -4922,
        10497,
        -20908,
        38973,
        -68026,
        111075,
        -169111,
        238522,
        -308360,
        360033,
        -373190,
        337618,
        -262546,
        173171,
        -95678,
        43693,
        -16222,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "multiplicity": 3376055
    },
    {
      "name": "R2",
      "coeffs": [
        1,
        -7,
        29,
        -86,
        202,
        -387,
        618,
        -861,
        1256,
        -2589,
        7105,
        -19328,
        45963,
        -93546,
        163248,
        -244838,
        315271,
        -347265,
        325506,
        -258092,
        171927,
        -95429,
        43661,
        -16220,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "multiplicity": 854210
    },
    {
      "name": "P7",
      "coeffs": [
        1,
        -3,
        8,
        -18,
        36,
        -62,
        97,
        -123,
        114,
        -73,
        31,
        -8,
        1
      ],
      "multiplicity": 4177785
    },
    {
      "name": "P9",
      "coeffs": [
        1,
        -4,
        10,
        -17,
        26,
        -47,
        119,
        -298,
        592,
        -878,
        963,
        -780,
        464,
        -199,
        59,
        -11,
        1
      ],
      "multiplicity": 14295157
    },
    {
      "name": "Ed5",
      "coeffs": [
        1,
        -7,
        29,
        -85,
        192,
        -332,
        398,
        -154,
        -644,
        1760,
        -1469,
        -4682,
        24307,
        -66045,
        133624,
        -218149,
        295447,
        -335304,
        319744,
        -255926,
        171313,
        -95305,
        43645,
        -16219,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "multiplicity": 6652059
    }
  ],
  "numerator": [
    {
      "name": "P1",
      "coeffs": [
        1,
        0
      ],
      "q_rational": "309690889482955/4194304"
    },
    {
      "name": "P2",
      "coeffs": [
        1,
        -1
      ],
      "q_rational": "630788667754879/8773059"
    },
    {
      "name": "P3",
      "coeffs": [
        1,
        1,
        -2,
        1
      ],
      "q_rational": "21260800937839/8055645"
    },
    {
      "name": "P4",
      "coeffs": [
        1,
        -2,
        4,
        -3,
        1
      ],
      "q_rational": "52745169098993/7487927"
    },
    {
      "name": "P6",
      "coeffs": [
        1,
        -3,
        8,
        -16,
        26,
        -27,
        17,
        -6,
        1
      ],
      "q_rational": "29007076082772/3169231"
    },
    {
      "name": "P8",
      "coeffs": [
        1,
        -3,
        7,
        -14,
        30,
        -58,
        96,
        -123,
        114,
        -73,
        31,
        -8,
        1
      ],
      "q_rational": "3410042187423/8533421"
    },
    {
      "name": "select2_1",
      "coeffs": [
        4,
        -38,
        207,
        -812,
        2561,
        -6945,
        17096,
        -39799,
        89771,
        -197701,
        424713,
        -887490,
        1795649,
        -3485465,
        6398181,
        -10924979,
        17088187,
        -24185149,
        30692169,
        -34694324,
        34759255,
        -30738091,
        23901687,
        -16278606,
        9667160,
        -4978627,
        2208233,
        -835925,
        266797,
        -70593,
        15115,
        -2525,
        310,
        -25,
        1
      ],
      "q_rational": "1992723892935/9974618"
    },
    {
      "name": "select2_11",
      "coeffs": [
        1,
        -6,
        21,
        -55,
        131,
        -304,
        687,
        -1464,
        2899,
        -5348,
        9380,
        -15914,
        25733,
        -37857,
        48221,
        -51383,
        44906,
        -31805,
        18072,
        -8135,
        2846,
        -750,
        141,
        -17,
        1
      ],
      "q_rational": "702728210855/1985031"
    },
    {
      "name": "select2_15",
      "coeffs": [
        4,
        -37,
        185,
        -648,
        1796,
        -4200,
        8568,
        -15384,
        23959,
        -30504,
        25432,
        7739,
        -86988,
        217437,
        -375779,
        510376,
        -566410,
        521243,
        -399737,
        255377,
        -135321,
        58971,
        -20847,
        5852,
        -1261,
        197,
        -20,
        1
      ],
      "q_rational": "450900060781/9270228"
    },
    {
      "name": "select2_22",
      "coeffs": [
        1,
        -8,
        38,
        -135,
        403,
        -1068,
        2605,
        -5960,
        12920,
        -26655,
        52399,
        -97773,
        171401,
        -278016,
        410164,
        -541424,
        630107,
        -638293,
        556602,
        -413746,
        259743,
        -136354,
        59146,
        -20866,
        5853,
        -1261,
        197,
        -20,
        1
      ],
      "q_rational": "6599318260539/9993640"
    },
    {
      "name": "select2_25",
      "coeffs": [
        1,
        -8,
        36,
        -122,
        360,
        -982,
        2513,
        -6061,
        13923,
        -30792,
        65918,
        -136287,
        269810,
        -505833,
        889653,
        -1457535,
        2207549,
        -3057902,
        3820947,
        -4244920,
        4139251,
        -3505831,
        2557595,
        -1595343,
        844525,
        -376078,
        139267,
        -42206,
        10227,
        -1912,
        260,
        -23,
        1
      ],
      "q_rational": "562420442071/2264313"
    },
    {
      "name": "select2_36",
      "coeffs": [
        2,
        -12,
        39,
        -83,
        140,
        -244,
        567,
        -1453,
        3167,
        -5350,
        6891,
        -6783,
        5120,
        -2959,
        1296,
        -420,
        96,
        -14,
        1
      ],
      "q_rational": "3362145432269/9532037"
    },
    {
      "name": "select3_7",
      "coeffs": [
        1,
        -7,
        29,
        -86,
        202,
        -394,
        682,
        -1175,
        2339,
        -5517,
        13684,
        -32030,
        67374,
        -125160,
        203975,
        -290291,
        358834,
        -382747,
        349760,
        -271796,
        178207,
        -97705,
        44290,
        -16345,
        4802,
        -1085,
        178,
        -19,
        1
      ],
      "q_rational": "4352002110254/4887323"
    },
    {
      "name": "select4_0",
      "coeffs": [
        2,
        -11,
        38,
        -100,
        236,
        -525,
        1122,
        -2287,
        4475,
        -8513,
        15749,
        -27545,
        43614,
        -60190,
        70581,
        -69225,
        56187,
        -37401,
        20212,
        -8747,
        2970,
        -766,
        142,
        -17,
        1
      ],
      "q_rational": "3578264620002/7819705"
    },
    {
      "name": "select4_1",
      "coeffs": [
        1,
        -12,
        82,
        -410,
        1668,
        -5835,
        18167,
        -51523,
        135356,
        -333458,
        777298,
        -1725418,
        3663238,
        -7459294,
        14587968,
        -27403609,
        49389031,
        -85190199,
        140115302,
        -218726258,
        322363057,
        -446054609,
        576169042,
        -690800673,
        764442941,
        -776461218,
        719994057,
        -606304602,
        461297021,
        -315497875,
        192973946,
        -104983402,
        50494997,
        -21323743,
        7840327,
        -2483849,
        668913,
        -150381,
        27514,
        -3945,
        417,
        -29,
        1
      ],
      "q_rational": "13531153728682/6884769"
    },
    {
      "name": "select4_3",
      "coeffs": [
        2,
        -21,
        130,
        -601,
        2292,
        -7570,
        22305,
        -59794,
        147980,
        -342157,
        746970,
        -1553723,
        3100204,
        -5956399,
        11023931,
        -19600803,
        33303530,
        -53682087,
        81388763,
        -114989182,
        149968319,
        -178911747,
        193620435,
        -188683997,
        164516560,
        -127623942,
        87631751,
        -52989574,
        28064629,
        -12937459,
        5151548,
        -1754646,
        504677,
        -120443,
        23263,
        -3503,
        387,
        -28,
        1
      ],
      "q_rational": "5381514591569/5240791"
    },
    {
      "name": "select5_0",
      "coeffs": [
        1,
        -9,
        46,
        -169,
        498,
        -1250,
        2796,
        -5753,
        11064,
        -19812,
        32308,
        -45633,
        47660,
        -2475,
        -182371,
        717403,
        -2019226,
        4786278,
        -9972238,
        18539162,
        -30925874,
        46347467,
        -62318031,
        74954460,
        -80337777,
        76416845,
        -64238867,
        47525833,
        -30809315,
        17415286,
        -8533944,
        3599009,
        -1294009,
        391694,
        -98105,
        19835,
        -3119,
        359,
        -27,
        1
      ],
      "q_rational": "4617249463684/4001225"
    },
    {
      "name": "select5_7",
      "coeffs": [
        1,
        -9,
        47,
        -178,
        546,
        -1435,
        3365,
        -7247,
        14643,
        -28089,
        51282,
        -88310,
        139578,
        -190080,
        187192,
        -16035,
        -499843,
        1533708,
        -3117428,
        5000910,
        -6649877,
        7468617,
        -7140762,
        5828720,
        -4061676,
        2410680,
        -1213098,
        513847,
        -181254,
        52412,
        -12138,
        2172,
        -283,
        24,
        -1
      ],
      "q_rational": "4710839667389/9906458"
    },
    {
      "name": "select5_9",
      "coeffs": [
        1,
        -9,
        50,
        -209,
        713,
        -2072,
        5352,
        -12819,
        29487,
        -66216,
        144586,
        -302281,
        595413,
        -1092236,
        1852367,
        -2887841,
        4111897,
        -5304068,
        6141384,
        -6323667,
        5740628,
        -4558782,
        3144106,
        -1869683,
        951064,
        -409891,
        147838,
        -43881,
        10465,
        -1934,
        261,
        -23,
        1
      ],
      "q_rational": "1079755879201/2164874"
    },
    {
      "name": "select5_10",
      "coeffs": [
        1,
        -9,
        49,
        -201,
        689,
        -2071,
        5629,
        -14110,
        33089,
        -73323,
        154532,
        -310646,
        595403,
        -1085220,
        1874469,
        -3057783,
        4695608,
        -6763343,
        9093118,
        -11334901,
        12986209,
        -13536379,
        12702011,
        -10620418,
        7837600,
        -5060078,
        2833453,
        -1363641,
        558141,
        -191760,
        54348,
        -12399,
        2195,
        -284,
        24,
        -1
      ],
      "q_rational": "6714480457493/8818907"
    },
    {
      "name": "select7_0",
      "coeffs": [
        1,
        -12,
        81,
        -396,
        1560,
        -5242,
        15586,
        -42076,
        105147,
        -246793,
        549796,
        -1170530,
        2390599,
        -4690319,
        8840994,
        -16000902,
        27776968,
        -46174342,
        73308008,
        -110741837,
        158439195,
        -213605148,
        270045695,
        -318741334,
        349886561,
        -355860580,
        333984684,
        -287859759,
        226553944,
        -161761596,
        104040100,
        -59821080,
        30502992,
        -13673698,
        5336261,
        -1792195,
        510634,
        -121137,
        23316,
        -3505,
        387,
        -28,
        1
      ],
      "q_rational": "9317325406677/3194929"
    },
    {
      "name": "select8_0",
      "coeffs": [
        1,
        -4,
        11,
        -25,
        60,
        -144,
        325,
        -671,
        1284,
        -2331,
        4097,
        -6881,
        10462,
        -13549,
        14349,
        -12162,
        8149,
        -4267,
        1717,
        -516,
        110,
        -15,
        1
      ],
      "q_rational": "10953669139763/9925694"
    },
    {
      "name": "select9_1",
      "coeffs": [
        1,
        -5,
        15,
        -36,
        91,
        -242,
        615,
        -1435,
        3129,
        -6489,
        12789,
        -23438,
        38586,
        -55116,
        66531,
        -66730,
        55026,
        -37005,
        20118,
        -8733,
        2969,
        -766,
        142,
        -17,
        1
      ],
      "q_rational": "3449087714362/9861087"
    },
    {
      "name": "select9_2",
      "coeffs": [
        1,
        -9,
        49,
        -201,
        689,
        -2067,
        5589,
        -13894,
        32271,
        -70887,
        148499,
        -297967,
        573242,
        -1055962,
        1856652,
        -3098818,
        4866114,
        -7097880,
        9459816,
        -11290297,
        11759588,
        -10278192,
        6952893,
        -2718671,
        -1069899,
        3361766,
        -3915291,
        3239422,
        -2114613,
        1125296,
        -492915,
        177386,
        -51890,
        12092,
        -2170,
        283,
        -24,
        1
      ],
      "q_rational": "4659890228461/8743052"
    },
    {
      "name": "select9_3",
      "coeffs": [
        1,
        -11,
        70,
        -330,
        1284,
        -4365,
        13417,
        -38044,
        100658,
        -250202,
        587295,
        -1308464,
        2781706,
        -5670378,
        11121283,
        -21013615,
        38213599,
        -66687973,
        111214968,
        -176359094,
        264474559,
        -372923379,
        491467994,
        -601609787,
        679730680,
        -704426605,
        665533653,
        -569942366,
        440000884,
        -304637294,
        188191489,
        -103183560,
        49923676,
        -21173462,
        7808376,
        -2478559,
        668271,
        -150330,
        27512,
        -3945,
        417,
        -29,
        1
      ],
      "q_rational": "6289381318901/9096035"
    },
    {
      "name": "select9_5",
      "coeffs": [
        1,
        -11,
        72,
        -355,
        1454,
        -5186,
        16578,
        -48430,
        131184,
        -333146,
        799904,
        -1827207,
        3988112,
        -8340337,
        16736892,
        -32237879,
        59551766,
        -105299761,
        177704166,
        -285130994,
        432968413,
        -618891522,
        827838369,
        -1029648232,
        1183007380,
        -1247348437,
        1199301252,
        -1045185205,
        820956344,
        -578041734,
        362906005,
        -202036186,
        99139817,
        -42583435,
        15877456,
        -5085431,
        1380353,
        -311777,
        57117,
        -8170,
        858,
        -59,
        2
      ],
      "q_rational": "651575276147/7044436"
    },
    {
      "name": "select9_6",
      "coeffs": [
        1,
        -9,
        49,
        -201,
        692,
        -2103,
        5827,
        -15008,
        36402,
        -83844,
        184343,
        -387820,
        781155,
        -1506486,
        2781747,
        -4913141,
        8269247,
        -13163298,
        19602707,
        -26964851,
        33828506,
        -38263650,
        38645499,
        -34574737,
        27219265,
        -18745167,
        11227890,
        -5812895,
        2582005,
        -974819,
        308964,
        -80818,
        17027,
        -2785,
        333,
        -26,
        1
      ],
      "q_rational": "11838421919974/8950455"
    },
    {
      "name": "select9_7",
      "coeffs": [
        2,
        -28,
        203,
        -1030,
        4145,
        -14217,
        43455,
        -121469,
        314404,
        -757762,
        1709873,
        -3647232,
        7456154,
        -14800622,
        28672199,
        -53844939,
        96519298,
        -162256961,
        252016106,
        -357831420,
        461324936,
        -537828113,
        565636876,
        -535808448,
        456559542,
        -349441936,
        239780014,
        -147118539,
        80423132,
        -38983624,
        16651949,
        -6217632,
        2008235,
        -553423,
        127734,
        -24061,
        3560,
        -389,
        28,
        -1
      ],
      "q_rational": "127103111402/1055161"
    },
    {
      "name": "select10_0",
      "coeffs": [
        1,
        -12,
        82,
        -407,
        1640,
        -5697,
        17700,
        -50282,
        132453,
        -326821,
        761875,
        -1690630,
        3591901,
        -7330752,
        14383482,
        -27104551,
        48960365,
        -84554446,
        139100272,
        -216848906,
        318160866,
        -435819847,
        552690546,
        -643690519,
        683542241,
        -657742145,
        570498725,
        -443982883,
        308717694,
        -191002089,
        104682340,
        -50567221,
        21398086,
        -7871767,
        2492772,
        -670722,
        150637,
        -27537,
        3946,
        -417,
        29,
        -1
      ],
      "q_rational": "4884194025059/4010746"
    },
    {
      "name": "select11_0",
      "coeffs": [
        1,
        -10,
        58,
        -247,
        863,
        -2628,
        7265,
        -18713,
        45623,
        -106162,
        236819,
        -507753,
        1048060,
        -2083858,
        3987619,
        -7324420,
        12859688,
        -21476680,
        33970535,
        -50764813,
        71702346,
        -96060690,
        122706725,
        -149997591,
        175165445,
        -193721483,
        200096863,
        -190082642,
        163761588,
        -126505547,
        86844853,
        -52592386,
        27909249,
        -12889531,
        5139982,
        -1752522,
        504396,
        -120419,
        23262,
        -3503,
        387,
        -28,
        1
      ],
      "q_rational": "6519687014701/5871539"
    },
    {
      "name": "merged_0",
      "coeffs": [
        1,
        -9,
        46,
        -168,
        491,
        -1227,
        2763,
        -5827,
        11812,
        -23325,
        45015,
        -84319,
        150986,
        -253902,
        395089,
        -563092,
        729524,
        -852796,
        891641,
        -825399,
        669151,
        -469815,
        282447,
        -143642,
        60934,
        -21182,
        5889,
        -1263,
        197,
        -20,
        1
      ],
      "q_rational": "3775427748764/6478995"
    }
  ],
  "credits": [
    "Doche: limit-point construction and original polynomial library",
    "Grinsztajn: starting perturbative denominator factors and public construction",
    "Epi/BakeLab: additional degree-28 denominator, degree-16 numerator, and unequal-multiplicity construction"
  ]
}