{ "description": "Doche limit-point construction; Epi additional factors and unequal multiplicities credited; union joint LP plus dual-guided numerator perturbations. Exact rational certificate.", "target": "0.25353524", "grid": 524288, "numeric_unverified": 0.253535232072136, "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": 17256956 }, { "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": 6768665 }, { "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": 3739372 }, { "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": 3928319 }, { "name": "P7", "coeffs": [ 1, -3, 8, -18, 36, -62, 97, -123, 114, -73, 31, -8, 1 ], "multiplicity": 1227044 }, { "name": "P9", "coeffs": [ 1, -4, 10, -17, 26, -47, 119, -298, 592, -878, 963, -780, 464, -199, 59, -11, 1 ], "multiplicity": 10338327 }, { "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": 6215959 } ], "numerator": [ { "name": "P1", "coeffs": [ 1, 0 ], "q_rational": "1291813008066787/8388608" }, { "name": "P2", "coeffs": [ 1, -1 ], "q_rational": "1110885635615413/8669273" }, { "name": "P3", "coeffs": [ 1, 1, -2, 1 ], "q_rational": "81029057433146/7955115" }, { "name": "P4", "coeffs": [ 1, -2, 4, -3, 1 ], "q_rational": "32765391765941/1831329" }, { "name": "P6", "coeffs": [ 1, -3, 8, -16, 26, -27, 17, -6, 1 ], "q_rational": "176698714954466/5976823" }, { "name": "P8", "coeffs": [ 1, -3, 7, -14, 30, -58, 96, -123, 114, -73, 31, -8, 1 ], "q_rational": "7633981735085/6376723" }, { "name": "En6", "coeffs": [ 1, -5, 19, -56, 134, -258, 420, -613, 831, -1006, 1009, -790, 465, -199, 59, -11, 1 ], "q_rational": "8437866674915/3860016" }, { "name": "broad1_3", "coeffs": [ 1, -7, 30, -97, 269, -678, 1608, -3615, 7663, -15240, 28538, -50734, 85966, -137853, 205672, -279548, 339163, -360855, 331764, -260366, 172556, -95554, 43677, -16221, 4786, -1084, 178, -19, 1 ], "q_rational": "2528340207903/6880708" }, { "name": "broad1_4", "coeffs": [ 1, -7, 29, -87, 215, -478, 1048, -2370, 5417, -11931, 24581, -46972, 83233, -136449, 205266, -279578, 339254, -360898, 331774, -260367, 172556, -95554, 43677, -16221, 4786, -1084, 178, -19, 1 ], "q_rational": "4845246269615/4289662" }, { "name": "broad1_6", "coeffs": [ 1, -4, 10, -18, 35, -83, 203, -424, 718, -962, 999, -789, 465, -199, 59, -11, 1 ], "q_rational": "5620211313181/7018043" }, { "name": "broad1_10", "coeffs": [ 1, -5, 17, -46, 109, -229, 435, -739, 1087, -1315, 1256, -923, 512, -209, 60, -11, 1 ], "q_rational": "15445337740698/3284323" }, { "name": "broad2_1", "coeffs": [ 1, -4, 9, -10, -3, 41, -93, 119, -79, -4, 60, -58, 29, -8, 1 ], "q_rational": "5838104778119/7975350" }, { "name": "broad2_2", "coeffs": [ 1, -5, 17, -46, 114, -259, 536, -969, 1466, -1781, 1685, -1215, 655, -257, 70, -12, 1 ], "q_rational": "2992906021892/1877335" }, { "name": "broad2_3", "coeffs": [ 1, -4, 11, -19, 29, -48, 110, -259, 514, -787, 897, -750, 456, -198, 59, -11, 1 ], "q_rational": "715446372436/6996231" }, { "name": "broad2_4", "coeffs": [ 1, -4, 10, -16, 21, -32, 84, -232, 497, -781, 896, -750, 456, -198, 59, -11, 1 ], "q_rational": "356505494553/3294146" }, { "name": "broad2_5", "coeffs": [ 1, -4, 11, -22, 36, -51, 88, -204, 447, -737, 873, -743, 455, -198, 59, -11, 1 ], "q_rational": "6771492362513/9036788" }, { "name": "broad2_6", "coeffs": [ 1, -4, 10, -17, 27, -52, 126, -290, 551, -814, 908, -752, 456, -198, 59, -11, 1 ], "q_rational": "1001751306583/2781669" }, { "name": "broad2_7", "coeffs": [ 1, -4, 11, -22, 44, -92, 201, -414, 789, -1392, 2270, -3316, 4122, -4167, 3328, -2060, 970, -338, 83, -13, 1 ], "q_rational": "2855510292356/1022477" } ] }